University
stringclasses 19
values | Text
stringlengths 458
20.7k
|
|---|---|
ADE | Figure 7.21 demonstrates the degradation of contact stiffness at the cement sheath interface
with the casing subjected to heating and cooling scenarios considering the three thermal rates
within the cement sheaths with 30% eccentricity.
As can be seen in Figure 7.21(a) the contact stiffness between the casing and the cement sheath
is fully degraded when subjected to instant heating which is again an indication of the detrimental
effect of instant heating. While for the controlled heating rates scenarios the degradation index
reaches one in particular section (almost at the centre of the selected path) of the interface. Figure
7.21 (b) shows debonding at the interfaces is not occurred yet in the cooling scenarios, although
at the starting and ending locations of the selected path the degradation index reaches 0.8 (which
means 80% of the contact stiffness is degraded).
(a) (b)
Figure 7.21: Contact Stiffness Degradation at the Interface of the 30% Eccentric Cement Sheaths with the
Casing Subjected to Heating and Cooling Scenarios
Figure 7.22 demonstrates the degradation of contact stiffness at the cement sheath interface
with the casing subjected to heating and cooling scenarios considering the three thermal rates
within the cement sheath with 70% eccentricity.
130 |
ADE | (a)
(b)
Figure 7.24: Contact Stiffness Degradation at the Interface of the 70% Eccentric Cement with the
Formation Subjected to Heating and Cooling Scenarios
Considering the damage index at the interfaces in Figure 7.24 shows the weakness of the
interfaces while subjected to mechanical and thermal loads in the cement sheath with 70%
eccentricity.
The interfaces are the most vulnerable parts of wells due to the high difference in the stiffness
of surrounding materials, and high contact shear stresses in tangential and normal directions of the
interfaces. The contact stiffness degradation reaches near to one in all the simulations signifies the
high potential of debonding at the interfaces. However, the occurrence of cement sheath
debonding from the casing prevents the stress transference from the casing to the cement,
therefore, it may prevent the incidence of cement sheath cracking and it may relax the stress regime
within the cement sheath. Cement sheath centralisation, remedial cementing and using expandable
liners (at the interfaces of cement and casing) may help to alleviate these kinds of problems.
7.7.Conclusion
A numerical approach was carried out to investigate the integrity of eccentric cement sheaths
after being subjected to mechanical and thermal well operational procedures in relation to the
creation of cracks within the cement sheath and the propensity of cement sheath interface
debonding. The importance of incorporating a comprehensive constitutive model (Concrete
Damage Plasticity model) for modelling geo-materials such as cementitious materials was shown.
133 |
ADE | The superiority of Concrete Damage plasticity model with respect to simulating different states of
damage by considering the different response of geo-materials to tensile and compression stress
state and consequently capability to reproduce experimental data were highlighted. This model
also considers the materials pressure-dependency behaviour under shearing at different levels of
confinement and dilatancy of the geo-materials by incorporating non-associated flow rule.
The integrity of the cement sheath was assessed based on the local compression and tensile
damage, and global damage indicators within the cement sheaths considering different mechanical
and thermal scenarios. The compression and tensile damage occurred on the narrowest side of the
cement sheaths in all the studied scenarios confirm the importance of casing centralisation.
The simulations results show employing controlled heating rates might lead to less potential
compression damage within the cement sheaths. The magnitude and localisation of tensile damage
are more dependent on the geometry of the wellbore rather than the heating rates.
In cooling scenarios (within the range studied) the magnitude of local and global compression
and tensile damage occurred within the cement sheaths are considerably lower than heating
scenarios. Moreover, the effects of different rates of cooling on the cement sheath damage are also
minimal due to the dominant effect of pressurizing the wellbore and in-situ stresses confinement.
The simulations result also show that the cement sheath interfaces with the casing and the
formation are potential weak points to provide zonal isolation.
To prevent damage occurring within the cement sheaths requires assessments and simulations
considering the specific features of each case. There are many influential factors which make
every case different than the others. The effect of cement and the surrounding mechanical and
thermal properties, different geometries and architectures of the wellbores, wellbore operational
procedures, the anisotropy of geological stress fields, and the complex behaviour of the interfaces
etc. are required to be investigated and implemented for each simulation.
134 |
ADE | 8. Conclusions
The cement sheath in oil and gas wells acts as the key barrier to provide complete zonal isolation
and prevents the undesired fluid migration to the surrounding environment. The cement sheath
integrity might be compromised due to the imposed pressure and temperature variations to the
wellbores during wellbores lifetime or even after wellbores are abandoned/decommissioned. The
cement sheath mechanical failure within a wellbore is influenced and controlled by many factors
including but not limited to cement mechanical properties, cement bonding strength, in-situ
stresses conditions, cement history (cement shrinkage), wellbore architecture, and wellbore
deviation. Due to the complications accompanied by each factor, it is of utmost importance to
include all the pertinent features into the predicting models with respect to the cement failure
mechanisms within the current state of the art.
To achieve the above goal, this thesis aimed to improve the modelling capabilities in cement
sheath integrity evaluations by employing a more comprehensive constitutive model (Concrete
Damage Plasticity model) compared to the rest of the models previously used. The superiorities
of Concrete Damage Plasticity model have been explained with respect to its abilities to embed
different states of damage (compression/shear and tensile), pressure sensitive yield criterion, and
the materials dilatancy (utilising non-associative flow rule). However, the paucity of cement class
G mechanical properties was an obstacle to perform precise numerical simulations in particular
data pertaining to the cement long-term mechanical properties and confinement dependent
strength. Therefore, in the experimental phase of this study, the corresponding constitutive model
parameters were obtained through performing confined, unconfined compression tests, and
indirect tensile tests (three-point bending tests) on specimens made out of cement class G. The
suitability and reliability of the intended model parameters were also calibrated and validated by
numerical simulations.
The effects of different influential factors including the anisotropy of in-situ stresses, different
stiffness’s of surrounding rocks, different degrees of casing eccentricity, and different mechanical
and thermal loading scenarios (heating rates/cooling rates) were investigated in the numerical
simulations. The significance of casing centralisation and elevated risks of cement mechanical
failure caused by wellbore operations in anisotropic in-situ stress fields with soft rocks were
highlighted. The simulations result also showed that the cement sheath subjected to controlled
heating rates might experience less potential compression damage comparing to cement sheath
subjected to instant heating. The magnitude and localisation of tensile damage were shown to be
more dependent on the geometry of the wellbore rather than the heating rates. In cooling scenarios,
135 |
ADE | the effects of wellbore contractions due to temperature reduction on the cement sheath integrity
were shown to be minimal due to the dominant effect of pressurizing the wellbore and in-situ
stresses confinement.
8.1.Research Contributions
This thesis improved the capabilities of predictive models for cement sheath integrity
assessments and addressed the limitations of the previous models and shortcomings in the cement
class G mechanical properties inventory. The specific research contributions to address the
research intentions are as follows.
• Objective 1- Evaluation of Cement Sheath Integrity Subject to Enhanced Pressure
(PAPER-1)
An experimental-numerical approach was developed to evaluate the integrity of the cement
sheath after being pressurised regarding the creation of cracks within the cement sheath and the
creation of micro-annuli. The key intention of the approach is the incorporation of Concrete
Damage Plasticity (CDP) constitutive model for the cement sheath. The CDP model especially
formulated for modelling geo-materials by considering the difference in tensile and compressive
material responses, the pressure-dependent material behaviour under shearing at different levels
of confinement, and the materials dilatancy.
The experimental studies including uniaxial compression tests and three-point bending tests
were performed on specimens manufactured from cement class G to obtain the corresponding
constitutive model parameters. The results indicate the paramount influence of eccentricity on the
distribution of stress within the cement sheath which highlights the significance of casing
centralisation. The scenarios simulating pressure enhancement events considering anisotropic in-
situ stress fields with soft rocks exhibit the elevated possibility of high global damage indicator in
crushing and cracking. The high magnitude of cracking index (tensile damage) verifies the
importance of including tensile failure mechanisms into the constitutive modelling. The
simulations also show that the material interfaces are potential weak points.
• Objective 2- Effect of Curing Conditions on the Mechanical Properties of Cement Class
G with the Application to Wellbore Integrity (PAPER-2)
The cement class G inventory lacks some important aspects of cement mechanical properties
which cause complications and uncertainties into the performance of numerical simulations. The
effect of curing conditions on the responses of cement class G in confined and unconfined
compression tests and the measurement of tensile properties including cement fracture energy was
136 |
ADE | neglected in the inventory. The aim of the experimental phase was to add these important values
to the cement class G inventory.
The confined and unconfined compression tests were performed on the on cylindrical
specimens with the size of 42×100 mm cured at different temperatures of 30oC and 70oC for 28
days. An appropriate loading rate was determined for unconfined (uniaxial) tests as the peak load
is shown to be rate dependent on uniaxial tests. The specimens showed a well-defined peak load,
followed by highly brittle post-peak behaviour. However, the peak load in confined (triaxial) tests
is almost independent of the loading rate in the range measured. Moreover, the maximum strength
of the samples increases greatly as the confining pressure increases. The specimens exhibited more
ductile behaviour in confined compression tests in which the gradient of the load-displacement
graph inclines towards a plateau by the end of the test.
The investigations on curing temperature effects showed by increasing the curing temperatures,
the compressive strength of the material decreases considerably. This is attributed to the
differences in the formation of calcium silicate hydrate (CSH) gels, due to an increase in the curing
temperature.
The highly brittle behaviour of the prismatic samples in three-point bending tests indicated that
some modifications were required to be able to measure cement fracture energy properly. To
modify the test set-up configuration, the displacement rate was controlled by opening the crack
mouth clip gauge instead of the crosshead displacement (which usually controls the displacement
rate in three-point bending tests). The axial displacement of the loading platen was measured using
two LVDTs installed on both sides of the beam specimens. These applied modifications prevent
highly brittle crack propagation and allow capturing the post-peak response and measuring the
fracture energy. The results obtained from the clip gauge were also validated by non-contact strain
measurement technique using two-dimensional Digital Image Correlation (DIC) technology
measurements. In this technique, surface images before and during the deformation are taken by
digital cameras. The deformation measurements were based on the displacements of random
speckles spread over the surface of the sample. To analyse the images after the test, an area of
interest (in the vicinity of the notch) was chosen in which to detect the deformations and strain
localizations. The surface displacement was computed by comparing the number of digital images
taken during the test with the reference image (undeformed image). The correlation computations
were based on tracing a set of pixels sited in deformed images.
The approximate shape of the loading/yield surface for elastoplastic models was obtained
utilising the experimental outcomes. The corresponding parameters for Concrete Damage
137 |
ADE | Plasticity were computed by curve fitting process and were validated by numerical analyses. The
obtained parameters improve the accuracy of Concrete Damage Plasticity model implementation
for cement sheaths in wellbores integrity simulations.
• Evaluation of Cement Sheath Integrity Reflecting Thermo-Plastic Behaviour of the
Cement in Downhole Conditions (PAPER-3)
Thermal-mechanical frameworks employing the Concrete Damage Plasticity model using the
obtained constitutive parameters (from the performed experiments on cement class G) were
developed to investigate the integrity of eccentric cement sheaths after being subjected to
mechanical and thermal loads due to different wellbore operational procedures. The interfaces
were modelled using surface-based cohesive behaviour accompanied by heat transfer behaviour.
The employment of surface-based cohesive behaviour instead of cohesive elements (commonly
used) allows the incorporation of thermal conduction behaviour as surface interaction properties
to overcome the limitation of the nonexistence of temperature degree of freedom in cohesive
elements. The integrity of the cement sheaths was assessed according to the local and global
damage indicators for compression and tensile damage within the cement sheaths considering
different degrees of eccentricity and different heating/cooling rates.
The results of heating simulations indicated that controlled heating rates might lead to less
potential compression damage. While the magnitude and localisation of tensile damage are more
dependent on the geometry of the wellbore rather than the heating rates. The results of cooling
scenarios (within the range studied) showed the lower magnitude of local and global compression
and tensile damage compared to the heating scenarios. In these scenarios, the contraction of
wellbore components (caused by temperature reduction) which pulls the wellbore components
towards the centre of the wellbore is counterbalanced with the applied pushing pressure at the
casing. Moreover, the effects of cooling rates on the cement sheath damage are also minimal due
to this dominant effect of pressurizing the wellbore. The low tensile damage magnitudes are
attributed to the dominant compressive effect of the applied mechanical load and the confinement
of in-situ stresses.
It is worth mentioning that preventing the occurrence of damage within the cement sheaths
requires investigation and assessments regarding each case specific characteristics. There are
many influential factors which indicate the studies should be done in the case by case basis. The
impact of cement and the surrounding mechanical and thermal properties, different geometries
and architectures of the wellbores, wellbore operational procedures, the heterogeneity of
138 |
ADE | geological stress fields, and the complicated response of interfaces, etc. are required to be
investigated for each case separately.
8.2.Research Limitations
In the numerical phase, uncertainties remain in the cement sheath integrity modelling
approaches owing to the complex interactions of the well components at the interfaces; the
adherence degree of cement to the surrounding materials is variable and dependent on each site
characteristic features including the mechanical characteristics of the rocks (formations), surface
finish of the casing, type of mud layer, and degree of mud removal, etc. The data required to
generate complex constitutive models (for both materials and the interfaces between them) in
addition to the variability of wellbore architectures, cement mix designs, cement curing regimes,
and operating conditions (monotonic and / cyclic operational procedures) indicates that the
assessment of wellbore integrity resumes a challenge.
8.3.Recommendations for future work
The paucity of experimental data that is required for measuring mechanical properties of well
cement corresponding to different curing conditions and mixed design still require attention. The
experimental phase of this research retains some limitations in terms of simulating the downhole
conditions at which cement cures, and the cement slurry formulation regarding lead and tail
cement. The curing conditions for cement (pressure and temperature) varies along a well length
as depth changes. Therefore, it is better for the cement specimens to be cured under different
pressure and temperature to imitate the downhole condition precisely. While in this research the
effect of curing temperature alone was examined on the samples made of only cement class G
without any additive. The limitations of the current research also represent opportunities for future
research, including developing an experimental framework with a special focus on simulating the
downhole curing condition along with the associated cement slurry design (lead and tail cement).
Moreover, developing regulated protocols to measure cement mechanical properties in particular
cement tensile properties is very important.
Developing a comprehensive model to predict cement sheath failure mechanisms in wellbores
is still a complicated task. Thus, working in some directions including the poro-plastic behaviour
of cement sheath, the effect of porosity, the cement adherence degree to different types of rock
formations, and cement mechanical failure under cyclic temperate and pressure variations may
lessen the complications in wellbore integrity assessments.
139 |
ADE | [97] T. Heinold, R.L. Dillenbeck, M.J. Rogers, The effect of key cement additives on the
mechanical properties of normal density oil and gas well cement systems, in: SPE Asia Pacific
Oil and Gas Conference and Exhibition, Society of Petroleum Engineers, 2002.
[98] R.L. Dillenbeck, G. Boncan, V. Clemente, M.J. Rogers, Testing cement static tensile behavior
under downhole conditions, in: SPE Eastern Regional Meeting, Society of Petroleum Engineers,
2005.
[99] T. Heinold, R.L. Dillenbeck, W.S. Bray, M.J. Rogers, Analysis of Tensile Strength Test
Methodologies For Evaluating Oil and Gas Well Cement Systems, in: SPE Annual Technical
Conference and Exhibition, Society of Petroleum Engineers, 2003.
[100] G. Quercia, D. Chan, K. Luke, Weibull statistics applied to tensile testing for oil well cement
compositions, Journal of Petroleum Science and Engineering, 146 (2016) 536-544.
[101] W. Weibull, A statistical distribution function of wide applicability, Journal of applied
mechanics, 18 (1951) 293-297.
[102] W. Morris, M.A. Criado, J. Robles, G. Bianchi, Design of high toughness cement for
effective long lasting well isolations, in: SPE Latin American and Caribbean Petroleum
Engineering Conference, Society of Petroleum Engineers, 2003.
[103] Z. Yuan, C. Teodoriu, J. Schubert, Low cycle cement fatigue experimental study and the
effect on HPHT well integrity, Journal of Petroleum Science and Engineering, 105 (2013) 84-90.
[104] M. Labibzadeh, B. Zahabizadeh, A. Khajehdezfuly, Early-age compressive strength
assessment of oil well class G cement due to borehole pressure and temperature changes, Journal
of American Science, 6 (2010) 1-7.
[105] J. Del Viso, J. Carmona, G. Ruiz, Shape and size effects on the compressive strength of
high-strength concrete, Cement and Concrete Research, 38 (2008) 386-395.
[106] F.K. Kong, R.H. Evans, Reinforced and prestressed concrete, CRC Press, 2014.
[107] M.K. Abd, Z.D. Habeeb, Effect of Specimen Size and Shape on Compressive Strength of
Self-Compacting Concrete, Diyala Journal of Engineering Sciences, 7 (2014) 16-29.
[108] M. Thiercelin, B. Dargaud, J. Baret, W. Rodriguez, Cement design based on cement
mechanical response, in: SPE annual technical conference and exhibition, Society of Petroleum
Engineers, 1997.
[109] D. Bentz, Transient plane source measurements of the thermal properties of hydrating
cement pastes, Materials and structures, 40 (2007) 1073-1080.
[110] A. Loiseau, Thermal Expansion of Cement and Well Integrity of Heavy Oil Wells, in: SPE
Heavy and Extra Heavy Oil Conference, Medellín, Colombia, 2014.
[111] G.E. King, D.E. King, Environmental Risk Arising From Well-Construction Failure--
Differences Between Barrier and Well Failure, and Estimates of Failure Frequency Across
148 |
ADE | Abstract
Stormwater harvesting (SWH) is an important water sensitive urban design (WSUD)
approach that provides an alternate water source and/or improves runoff quality through
stormwater best management practice technologies (BMPs).
Through integrated SWH system design at the development scale practitioners must
account for trade-offs between cost, harvested volume, and water quality improvement
performance which are usually dependent on design decisions for the type, size, and
spatial distribution of BMPs. In catchment management planning, additional objectives
such as catchment vegetation improvement and public recreation benefit need to be
maximized for a catchment region within a limited budget. As such, planning and design
of SWH systems with distributed BMPs is a complex problem that requires optimal
allocation of limited resources to maximize multiple benefits.
In this thesis, two innovative formal optimization approaches are presented for
formulating and identifying optimal solutions to problems requiring distributed BMPs.
Firstly, a multiobjective optimization framework is presented and applied to a case study
for the conceptual design of integrated systems of BMPs for stormwater harvesting. The
aim of this work is to develop a conceptual design modelling framework that handles the
optimal placement of stormwater harvesting (SWH) infrastructure within an urban
development. The framework produces preliminary SWH system designs representing
optimal trade-offs between cost, water harvesting, and water quality improvement
measures.
Secondly, a many (>3) -objective optimization framework is presented and applied to a
case study for catchment planning requiring the selection of a portfolio of distributed
BMP projects. The framework produces portfolios that are optimal with respect to four
objectives, and enables exploration of the many-objective trade-off surface using
interactive visual analytics. In addition, a multi-stakeholder method is presented, which
enables catchment managers and local government authorities to identify solutions that
represent a compromise between 16 objectives and eight optimization problem
representations using interactive visual analytics to encourage a negotiated solution.
vi |
ADE | Statement of Originality
I certify that this work contains no material which has been accepted for the award of any
other degree or diploma in any university or other tertiary institution and, to the best of
my knowledge and belief, contains no material previously published or written by another
person, except where due reference has been made in the text. In addition, I certify that
no part of this work will, in the future, be used in a submission for any other degree or
diploma in any university or other tertiary institution without the prior approval of the
University of Adelaide and where applicable, any partner institution responsible for the
joint-award of this degree.
I give consent to this copy of my thesis when deposited in the University Library, being
made available for loan and photocopying, subject to the provisions of the Copyright Act
1968.
The author acknowledges that copyright of published works contained within this thesis
(as listed below) resides with the copyright holder(s) of those works.
Di Matteo, M., Dandy, G.C. & Maier, H.R., 2017. Multiobjective optimization of
distributed stormwater harvesting systems. Journal of Water Resources Planning and
Management, 10.1061/(ASCE)WR.1943-5452.0000756.
I also give permission for the digital version of my thesis to be made available on the web,
via the University’s digital research repository, the Library catalogue and also through
web search engines, unless permission has been granted by the University to restrict
access for a period of time.
Signed:………………………………………...…Date:………………….
viii |
ADE | Glossary
Best Management Practices (BMPs), or stormwater best management practices, are
structural or non-structural technologies used to detain, harvest, infiltrate, evaporate, and
transport urban stormwater runoff, and remove pollutants. BMPs in stormwater
harvesting systems typically include wetlands, biofiltration devices, storage ponds, tanks,
and basins located near runoff sources or near an integrated catchment outlet
Biofiltration systems (biofilters) are stormwater treatment devices that typically
consist of a vegetated basin overlaying a geomembrane-lined or free-draining filter
medium with a drainage pipe at the bottom. Water biofiltration is the process of improving
water (stormwater and wastewater) quality by filtering water through biologically
influenced media (Payne, Hatt et al., 2015).
Constraints can be either hard or soft. Hard constraints set firm limits on the values
of the decision variables that are required to be satisfied or limit the possible solutions to
the problem. Soft constraints have some decision variable values that are penalized in the
objective function if certain conditions on the variables are not satisfied. The amount of
the penalty can be fixed or can depend on the extent to which the condition is violated.
Decision variable is a quantity that the decision-maker controls.
Formal optimization refers to finding the best solution from all feasible solutions of
a problem where the decision variables, objectives and constraints are mathematically
formulated.
Many-objective optimization is an optimization problem with four or more
objectives (Purshouse and Fleming 2007).
Multi-objective optimization (also multiobjective optimization) refers to an
optimization problem with two or more objectives. Typically, the Pareto front consists
of more than one solution, and as such trade-offs between objective function values often
exist for Pareto optimal solutions.
Non-dominated solution is a member of a set of solutions where none of the
objective functions can be improved in value without degrading one or more of the other
objective values (Purshouse, Deb et al. 2014).
xv |
ADE | Objective function (formal objective) is a function of the decision variables that is to
be maximised or minimised. It is usually expressed in mathematical terms.
Pareto optimal solution is a member of the Pareto front.
Pareto front (sometimes called non-dominated solution set, or Pareto optimal
solution set), is the set of non-dominated solutions to a multi-objective optimization
problem. A solution is sometimes called non-dominated, Pareto optimal, Pareto efficient
or noninferior if it is a member of the Pareto front.
Sediment basins are deep open-water ponds designed to facilitate settlement of
suspended particles from stormwater runoff.
Swales are linear, depressed channels that collect and transfer stormwater. They can
be lined with grass or more densely vegetated and landscaped. Swales can provide
physical screening of sedimentation (coarse and fine) and/or infiltrate stormwater into
soils.
Visual Analytics is “an iterative process that involves information gathering, data
preprocessing, knowledge representation, interaction and decision making. The ultimate
goal is to gain insight in the problem at hand which is described by vast amounts of data
from heterogeneous sources (Keim, Andrienko et al. 2008).”
Water Sensitive Urban Design (WSUD), in Australia, is “commonly used to reflect
the paradigm in the planning and design of urban environments that is ‘sensitive’ to the
issues of water sustainability and environmental protection.” In particular, it pertains to
the “interactions between the urban built form (including urban landscapes) and the urban
water cycle (as defined by the conventional urban water streams of potable water,
wastewater, and stormwater) (Wong 2006).” Similar concepts include Sustainable
Drainage Systems (SuDS), used in the United Kingdom, and Low Impact Development
(LID), used in the United States.
Wetlands (constructed wetlands) are shallow, extensively vegetated basins that use
enhanced sedimentation, fine filtration and pollutant uptake processes to remove runoff
pollutants.
xvi |
ADE | CHAPTER 1
Introduction
The future economic, environmental and social prosperity of urban environments
hinges upon effective management of urban water sources (Walsh, Fletcher et al. 2005).
Demand for clean water supply in urban areas increases with urban population growth,
resulting in water shortages and other supply security risks (Cook and Bakker 2012). In
addition, urban stream health is degraded by untreated stormwater runoff from developed
areas. This is due to increased generation of pollutants through urban land use and
pollutant mobilisation and transport of runoff volumes along impervious drainage
channels (Wong 2006). Urban stream health is further impacted by increases in the
volume of runoff and alteration to the pre-development flow regime that comes with the
introduction of paved surfaces. The impact of urban development is influential at multiple
spatial scales. These may range from degraded stream health within developments, to the
introduction of nutrients into marine bodies receiving flows from a large regional
catchment, and local to city-wide water supply security. Consequently, urban water
management strategies need to mitigate multiple economic, environmental and social
impacts targeted at multiple spatial scales where possible.
1.1 Background on Water Sensitive Urban Design (WSUD) systems
Modern urban stormwater management approaches, such as Water Sensitive Urban
Design (WSUD), including similar concepts such as Sustainable Drainage Systems
(SuDS) and Low Impact Development (LID), aim to mitigate impacts of development on
urban water sources (Askarizadeh, Rippy et al. 2015). To achieve this, WSUD uses
integrated systems of structural and non-structural stormwater best management practice
technologies (BMPs) for detention, harvesting, infiltration, evaporation, and transport of
urban runoff (Lerer, Arnbjerg-Nielsen et al. 2015). An increasingly popular WSUD
technique is urban stormwater harvesting (SWH), which is used to capture, store, treat
and distribute surface stormwater runoff for later reuse (Mitchell, Deletic et al. 2007).
SWH can provide a cost-effective and reliable alternative water supply source for
irrigation that reduces stormwater runoff volumes and complements existing (often
1 |
ADE | stressed) water supplies (Clark, Gonzalez et al. 2015, Marchi, Dandy et al. 2016). SWH
systems comprise BMPs that detain, harvest, infiltrate, evaporate, and transport urban
runoff, and remove pollutants. BMPs in SWH systems typically include wetlands,
biofiltration devices, storage ponds, tanks, and basins located near runoff sources or near
an integrated catchment outlet (Askarizadeh, Rippy et al. 2015).
BMPs integrated into the urban environment though WSUD approaches can provide
multiple human and ecosystem co-benefits (Mitchell, Deletic et al. 2007). Given the
possibility to maximize multiple benefits, objectives for WSUD planning and design
approaches include i) minimizing economic costs (Taylor and Wong 2002); ii)
maximizing the volume of harvested water, which can improve urban water supply (Clark
et al. 2015); iii) maximizing improvements in urban flow regimes by restoring stormwater
a) runoff quality and b) the streamflow regime (base flow, peak flow, annual runoff
volume, and flow variability) to be closer to pre-development conditions, thereby
promoting urban stream health (Askarizadeh, Rippy et al. 2015); and iv) maximizing
social benefits (Mitchell, Deletic et al. 2007), such as public amenity, community
acceptance, recreation, and reduced construction risks (Inamdar 2014, Sharma, Pezzaniti
et al. 2016). Which of the above objectives should be considered is case study specific
and generally determined through stakeholder consultation (for example, between
regulators, land developers, designers and the local community). In many instances, the
above objectives are in conflict with one another, necessitating decision-makers to
consider trade-offs between objectives when assessing the performance of WSUD
systems.
1.2 Multiobjective optimization for planning and design of WSUD
systems
Despite the potential to achieve multiple benefits using WSUD approaches, there are
always limited resources to achieve them. Compounding this difficulty are the multiple
possible spatial scales at which BMPs can be distributed throughout a catchment, the large
number of different types of system components and interaction between components,
and the large number of decision options (e.g. size, type and location of BMPs) and
therefore large number of possible solutions. Therefore, many WSUD planning and
design tasks can be formulated as multiobjective optimization problems (Purshouse and
2 |
ADE | Fleming 2007, Purshouse, Deb et al. 2014), where a set of decisions needs to be selected
to achieve multiple objectives (including minimizing cost) that meet a set of practical
constraints. There are a multitude of problems, at varying spatial scales, that need to be
considered in the planning and design of WSUD systems, and it is difficult to select an
optimal management solution that maximizes benefits. The particular problems addressed
in this thesis, and their features, are as follows:
1. Optimizing stormwater harvesting systems design. Designing systems of
BMPs for stormwater management, including harvesting, is complex because
practitioners need to consider:
a. multiple, often competing, objectives
b. different types of system components
c. the spatial distribution of components
d. a large number of design options.
2. Integrated catchment plan optimization. The issues with complex BMP
systems are compounded where multiple BMP systems distributed over a large
region need to be selected for a management strategy, for example in an
integrated catchment management plan to achieve multiple regional catchment
objectives. Decision support approaches for catchment management should be
able to:
a. handle several objectives
b. consider the full trade-off space of possible solutions
c. develop “trusted” solutions based on current modelling practice.
3. Optimization involving multiple stakeholders. Where multiple stakeholder
groups are responsible for the funding and operation of BMP systems over a
large region, it is difficult to identify catchment plans that compromise the
costs and benefits between all parties equitably, which encourages ‘buy-in’
into the adopted solution. Adapting decision-making approaches, in particular
optimization approaches, to account for different stakeholder groups is
difficult because:
a. stakeholders have different value sets and interests, making it difficult
to arrive at a consensus on one mathematical formulation that all
stakeholders will accept, which may affect how likely it is that
3 |
ADE | stakeholders will trust the optimization process and buy-into suggested
solutions
b. exploration and analysis of optimization solutions should enable
stakeholder engagement and expert input
c. the non-intuitive nature of multi-dimensional value analysis and
unanticipated and emergent trends can further prevent decision-makers
from understanding and trusting optimization results
d. the optimization framework used should facilitate a final negotiated
outcome and/or exploration of resource management alternatives to be
considered further.
The challenges identified in the previous optimization and decision support literature
addressing these three problems, and opportunities for solving them in new ways, are
discussed in more detail below.
1.2.1 Optimizing stormwater harvesting systems design
Considering the design of stormwater harvesting systems, given the large number of
types of system components, the many different ways in which they can be distributed
spatially and the large number of available design choices, it is difficult to identify
distributed BMP planning and design outcomes that are optimal with respect to the desired
competing objectives. Consequently, there is a need for an integrated framework that
considers all of the above factors in a holistic fashion. Given the potentially large number
of options, incorporation of a formal optimization approach (for example, using an
optimization algorithm) in such a framework is also likely to be of significant value.
However, previous studies in this field are limited, have not presented an integrated
approach, and have only considered a subset of the above factors. For example, Sample
and Heaney (2006) considered the impact on net present value of the size and spatial
distribution of integrated infiltration basins and irrigation systems, but did not consider
multiple objectives, nor a formal optimization approach. While Browne, Breen et al.
(2012) and Inamdar (2014) considered multiple objectives in conjunction with a range of
BMP alternatives for various SWH projects within a region, they also did not utilize
formal optimization approaches, making it unlikely that the solutions that provide the best
trade-offs among objectives were identified. In contrast, Marchi, Dandy et al. (2016) used
a formal multiobjective optimization technique to design surface runoff SWH system
4 |
ADE | components (the dimensions of a wetland, detention basins, and aquifer storage transfer
infrastructure). However, they did not consider how trade-offs were influenced by a mix
of different BMP alternatives for the capture, treatment, and storage of surface runoff,
optimal locations for BMPs within a catchment, or water quality improvement as a formal
objective. Formal optimization methods have also been used to identify the optimal mix,
size, and location of distributed BMPs (Perez-Pedini, Limbrunner et al. 2005, Maringanti,
Chaubey et al. 2009, Lee, Selvakumar et al. 2012), but these studies have not considered
SWH.
1.2.2 Integrated catchment plan optimization
For integrated catchment management planning, decision support approaches need to
handle several objectives, consider the full trade-off space, and develop trusted solutions
based on current modelling practice. However, current approaches have failed to meet all
of these needs. While existing multi-criteria decision analysis (MCDA) (Goicoechea,
Hansen et al. 1982, Hyde and Maier 2006) methods allow many performance criteria to
be considered when selecting a portfolio of BMPs (Ellis, Deutsch et al. 2006, Moglia,
Kinsman et al. 2012, Jia, Yao et al. 2013, Aceves and Fuamba 2016a, Aceves and Fuamba
2016b), and have been accepted in practice (Moglia, Kinsman et al. 2012), they require
decision-makers to define their preferences without knowledge of the full-trade-off
patterns between portfolios. Many-objective optimization approaches (Purshouse and
Fleming 2007) overcome this limitation since they produce an approximation of the
Pareto front (i.e. solutions to the problem where none of the objective functions can be
improved in value without degrading one or more of the other objective values
(Purshouse, Deb et al. 2014)), which allows an exploration and analysis of a large number
of portfolios to identify solutions that represent a desirable compromise between
performance criteria. However, many-objective optimization approaches can be
computationally expensive and produce a large number of solutions to select from
(Purshouse and Fleming 2007, Purshouse, Deb et al. 2014), which is why existing
catchment management simulation-optimization approaches have considered only a
limited number of objectives including cost and water quality improvement (Lee,
Selvakumar et al. 2012, Chichakly, Bowden et al. 2013, Chen, Qiu et al. 2015, Zou,
Riverson et al. 2015). In addition, simulation-optimization based approaches may not be
feasible within a catchment management authority’s planning capacities (Moglia,
5 |
ADE | Kinsman et al. 2012), complementary to existing practices, nor desirable if decision-
makers do not trust the solutions developed by the optimization algorithm.
Furthermore, while it is important to consider many objectives, as well as trade-offs
between them (rather than having pre-defined weights, as in MCDA), this makes the
analysis of many-objective optimization results difficult. This is because: (1) visualizing
the trade-offs between objectives in more than three dimensions can be cumbersome, (2)
many-objective Pareto fronts can have large numbers of non-dominated (i.e. none of the
objective functions can be improved in value without degrading one or more of the other
objective values) solutions, as the number of Pareto optimal solutions grows
exponentially with the number of formal objectives (Hughes 2005, Keim, Andrienko et
al. 2008), (3) human decision makers have a limited cognitive load and can select between
only a small number of solutions at a time (Miller 1956); this requires techniques to reduce
the Pareto frontier to a sub-set of diverse and promising solutions to present to decision-
makers, and (4) visualizing solution performance separately from decision options may
cause decision maker biases (Kasprzyk, Reed et al. 2012, Giuliani, Herman et al. 2014,
Matrosov, Huskova et al. 2015). Recently, advanced interactive visual analytics (Keim,
Andrienko et al. 2008) approaches have been applied to help humans make sense of large
and complex data sets such as those generated by many-objective optimization (Kasprzyk,
Reed et al. 2009). However, these approaches have not been applied in the catchment
management optimization literature.
1.2.3 Optimization involving multiple stakeholders
In previous research, there has been little focus on adapting optimization frameworks
to make them useful for stakeholder groups in real-life problem solving (Maier, Kapelan
et al. 2014). However, there has been some progress in relation to this in recent years,
including:
• The use of iterative approaches, which has allowed for multiple formulations
of the decision variables, objectives and constraints to be developed to
progressively better define optimization problems and provide an opportunity
for stakeholders to learn about the problem (Kollat and Reed 2007, Woodruff,
Reed et al. 2013, Piscopo, Kasprzyk et al. 2015, Wu, Maier et al. 2016).
6 |
ADE | • The development of an optimization framework that provides opportunities
for stakeholders to provide input into the various stages of optimization
studies, including problem definition, the optimization process, and final
decision-making (Wu, Maier et al. 2016).
• The development of many-objective optimization approaches, as a result of
advances in optimization algorithm performance, which identify solutions to
complex problems that represent the optimal trade-off between numerous (>3)
objectives to better capture stakeholder values (Kollat, Reed et al. 2011,
Kasprzyk, Reed et al. 2012, Woodruff, Reed et al. 2013, Cruz, Fernandez et
al. 2014, Chand and Wagner 2015, Hadka, Herman et al. 2015, Matrosov,
Huskova et al. 2015, Borgomeo, Mortazavi-Naeini et al. 2016, Woodruff
2016).
• The use of visual analytics approaches to better communicate the outputs of
optimization studies to stakeholders to help with exploration and analysis of
the trade-offs between objectives, to identify the impact of decisions on
performance, and ultimately select trusted solutions for further consideration
(Kollat and Reed 2007, Kollat, Reed et al. 2011, Woodruff, Reed et al. 2013,
Hadka, Herman et al. 2015, Matrosov, Huskova et al. 2015, Borgomeo,
Mortazavi-Naeini et al. 2016, Woodruff 2016). Visual analytics approaches
can include the use of interactive software package that allows multiple
visualisations of the same data set in high-dimensional plots. This enables the
data set to be explored and analysed rapidly. Techniques to explore and
analyse data include dynamic filtering to eliminate undesirable solutions,
interactive brushing, and multiple linked plots,
These advances have made optimization approaches more applicable to complex, real-
world problems with multiple stakeholders and many objectives. However, in previous
studies, the optimization problem to be solved has generally been represented by a single
formulation, including all decision variable options, objectives and constraints deemed to
be important. This can result in the inclusion of a large number of objectives and decision
variable options, making it difficult to identify solutions that represent the best trade-offs
between objectives (i.e. the solutions on the Pareto front), as mentioned in the previous
section. This is because the number of solutions required to characterise the Pareto front
increases exponentially as the number of objectives increases, thus making this process
7 |
ADE | very computationally expensive and beyond the capability of current optimization
algorithms (Cruz, Fernandez et al. 2014, Purshouse, Deb et al. 2014). In addition, despite
the recent advances in visual analytics approaches mentioned above, the inclusion of a
large (e.g. >10) number of objectives makes the identification of solutions that provide
acceptable trade-offs for different stakeholders extremely difficult, as this can be
cognitively challenging for decision-makers faced with large solution sets (Purshouse and
Fleming 2007).
In order to address the above difficulties, an innovative approach for identifying
stakeholder-driven, optimal compromise solutions is proposed for problems with distinct
stakeholder groups with potentially competing sets of objectives. An example of this
would be the integrated management of a river system and its catchment, where the
objectives of stakeholders managing separate sub-areas of the catchment would most
likely be different from each other, and different from those of stakeholders concerned
with managing the catchment as a whole. For example, stakeholders may weigh the
importance of water quality, runoff volume and volume harvested differently. As part of
the proposed approach, the overall optimization problem is represented as a series of
smaller, interconnected optimization problems, reflecting individual stakeholder sets and
interests. The Pareto optimal solutions resulting from this analysis provide the input into
a collaborative, multi-stakeholder negotiation process, as part of which visual analytics
are used to identify trusted and accepted compromise solutions. A key feature of the
proposed approach is the use of ‘best alternative to negotiated agreement (BATNA)’
solutions as a benchmark during the collaborative negotiation process. These are the
solutions that individual stakeholder groups would implement if they were to act in
isolation. This has been shown to increase the efficiency with which negotiated
compromise solutions can be achieved (Fitzgerald and Ross 2013, Fitzgerald and Ross
2015, Fitzgerald and Ross 2016).
1.3 Research objectives
In order to address the problems outlined above, this thesis develops general
optimization frameworks for the selection of stormwater best management practices
(BMPs), firstly for the optimal preliminary design of stormwater harvesting systems and
secondly for selecting a portfolio of BMPs for an integrated catchment management plan.
8 |
ADE | As part of the frameworks, mathematical optimization formulations are presented and are
solved using multiobjective metaheuristic algorithms. Visual analytics approaches are
used to identify trade-offs in objective and decision spaces. Furthermore, a multi-
stakeholder optimization framework is presented, which uses visual analytics to assist
with determining a negotiated solution to a complex integrated catchment management
problem. Overall, this study has the following three main objectives:
Objective 1: To develop a generic multiobjective optimization framework for conceptual
design of stormwater harvesting systems with components distributed throughout a
development-scale catchment (Paper 1).
Objective 2: To develop a generic optimization framework for selecting a portfolio of
stormwater best management practices (BMPs) to assist in regional integrated catchment
management decision-making (Papers 2 and 3).
Objective 2.1: To present a formal optimization approach that identifies the best
combinations of BMPs for many (> 3) objective integrated catchment planning (Paper 2).
Objective 2.2: To implement the optimization framework in Objective 2.1 in a multi-
stakeholder optimization-visualisation framework that is geared towards the identification
of negotiated compromise solutions for problems with multiple stakeholders with distinct
sets of objectives (Paper 3).
Objective 3: To evaluate the utility of the frameworks in Objectives 1 and 2 by applying
them to relevant case studies (Papers 1, 2 and 3).
Objective 3.1: To apply the framework in Objective 1 to a case study for stormwater
harvesting system design for a new housing development in Northern Adelaide, South
Australia (Paper 1).
Objective 3.2: To apply the framework in Objective 2.1 to a real-world case study
based on a single-stakeholder integrated catchment management plan for a major city in
Australia (Paper 2).
Objective 3.3: To apply the framework in Objective 2.2 to a real-world case study
based on a multi-stakeholder integrated catchment management plan for a major city in
Australia (Paper 3).
9 |
ADE | 1.4 Thesis overview
This thesis is organized into five chapters, with the main contributions being presented
in Chapters 2 to 4. Each of these chapters is presented in the form of a technical paper.
The first of these (Chapter 2) has been published in Journal of Water Resources Planning
and Management.
Chapter 2 introduces a generic framework for the conceptual design of SWH systems
that considers multiple objectives, a range of BMP types and their design options, the
spatial distribution of BMPs, and a formal optimization approach for identifying designs
that represent near-globally optimal trade-offs among competing objectives in an
integrated fashion (Objective 1). The utility of the framework is then illustrated (Objective
3) by applying it to a case study SWH system for a residential development in Adelaide,
South Australia (Objective 3.1).
Chapter 3 introduces an optimization framework for many-objective (i.e. >3
objective) integrated catchment management (Objective 2) for a single catchment
management authority. This features the use of an interactive visual analytics approach to
identify promising solutions. The utility of the approach is demonstrated on a case study
for an integrated catchment management plan for a region of a major Australian city
(Objective 3.1 and 3.2). The case study is used to demonstrate the benefits of the approach
by investigating the possible many-objective trade-offs between lifecycle cost, water
quality improvement, stormwater harvesting capacity and urban vegetation and amenity
improvement, and the importance of a many-objective approach compared to a bi-
objective water quality-cost optimization, as has been undertaken in previous studies
(Objective 3.2).
Chapter 4 introduces an optimization-visual analytics framework for complex
environmental management problems (Objective 2) involving multiple stakeholders
(Objective 2.2), incorporating the optimization approach developed in Chapter 3. In the
approach, the problem is represented as a series of smaller, interconnected optimization
problems, reflecting individual stakeholder sets and interests. The approach features
interactive visual analytics used to explore and analyse optimization results, and an
approach to reframe visualizations to encourage stakeholder negotiation. To demonstrate
the utility of the framework, it is applied to a realistic case study which involves multiple
10 |
ADE | Table 1-1 Linking of each of the papers to the objectives
Objectives Paper 1 Paper 2 Paper
3
1 To develop a generic multiobjective optimization framework for conceptual design of stormwater harvesting X
systems with components distributed throughout a development-scale catchment.
2 To develop a generic optimization framework for selecting a portfolio of stormwater best management X X
practices (BMPs) to assist regional integrated catchment management decision-making.
2.1 To present a formal optimization approach that identifies the best combinations of BMPs for many (> 3) X
objective catchment planning.
2.2 To implement the optimization framework in Objective 2.1 in a multi-stakeholder optimization- X
visualisation framework that is geared towards the identification of negotiated compromise solutions for
problems with multiple stakeholders with distinct sets of objectives.
3 To evaluate the utility of the frameworks in Objectives 1 and 2. X X X
3.1 To apply the framework in Objective 1 to a case study for stormwater harvesting system design for a new X
housing development in Northern Adelaide, South Australia
3.2 To apply the framework in Objective 2.1 to a real-world case study based on a single-stakeholder X
integrated catchment management plan for a major city in Australia.
3.3 To apply the framework in Objective 2.2 to a real-world case study based on a multi-stakeholder integrated X
catchment management plan for a major city in Australia.
12 |
ADE | Abstract
Stormwater harvesting (SWH) is an important water sensitive urban design (WSUD)
approach that provides an alternate water supply source and improves runoff quality
through integrated systems of stormwater best management practice (BMP) technologies.
In SWH system design, practitioners must account for trade-offs between cost, supply
volume, and water quality improvement performance, which are dependent on design
decisions for the type, size, and spatial distribution of BMPs. As such, design of SWH
systems with distributed BMPs is a complex, multiobjective optimization problem with a
large decision space. This paper presents a multiobjective optimization framework to
assess trade-offs in spatially distributed SWH system designs. The framework was
applied to a case study for a housing development in Adelaide, South Australia. Results
illustrated the potential benefits of distributing BMPs in an integrated SWH system where
space at the catchment outlet is limited. Trade-offs between volumetric reliability and
total suspended solids (TSS) reduction indicate large gains in TSS reduction can be
achieved with limited reduction in volumetric reliability. Concept designs in low-
cost/moderately reliable and low-cost/high TSS reduction trade-off regions contained
biofilters in locations receiving large inflows.
Author Keywords: stormwater harvesting, optimization, BMP, biofilter, wetland,
water-sensitive urban design (WSUD), sustainable drainage systems (SuDs), low impact
development (LID), green infrastructure, genetic algorithm, MUSIC
2.1 Introduction
Recently, the application of Water Sensitive Urban Design (WSUD) has demonstrated
an ability to mitigate the impacts of development on urban water supply security and
natural ecosystem health (Askarizadeh, Rippy et al. 2015). An increasingly popular
WSUD technique is urban stormwater harvesting (SWH), which is used to capture, treat,
store and distribute surface stormwater runoff for later reuse (Mitchell, Deletic et al.
2007). SWH can provide a cost-effective and reliable alternative water supply source for
irrigation that reduces stormwater runoff volumes and complements existing (often
stressed) water supplies (Clark, Gonzalez et al. 2015, Marchi, Dandy et al. 2016). SWH
18 |
ADE | systems are comprised of best management practice (BMP) technologies that detain,
harvest, infiltrate, evaporate, and transport urban runoff, and remove pollutants. BMPs in
SWH systems typically include gutters, pipes, drainage channels, wetlands, biofiltration
devices, storage ponds, tanks, and basins located near runoff sources or near an integrated
catchment outlet (Askarizadeh, Rippy et al. 2015). Although SWH systems can
incorporate flood control measures (Mitchell, Deletic et al. 2007), peak flood flows
typically bypass SWH system components that are designed separately for water quality
control. Planning and designing urban SWH systems is complex because practitioners
need to consider: i) multiple, often competing, objectives; ii) different types of system
components; iii) the spatial distribution of these components; and iv) a large number of
design options, as detailed below.
Potential SWH system design objectives include: i) minimizing costs (Taylor and
Wong 2002); ii) maximizing the volume of harvested water, which can improve urban
water supply (Clark, Gonzalez et al. 2015); iii) maximizing the amount of pollutant
removed, which is achieved by treating stormwater prior to harvesting, and by removing
pollutants in the harvested water supply; iv) maximizing improvements in urban
hydrology by restoring stormwater runoff quality and the streamflow regime (e.g., base
flow, peak flow, annual runoff volume, and flow variability) closer to pre-development
conditions, thereby promoting urban stream health (Askarizadeh, Rippy et al. 2015); and
v) maximizing social benefits (Mitchell, Deletic et al. 2007), such as public amenities,
community acceptance, recreation, and reducing construction risks (Inamdar 2014).
Which of the above objectives are considered and which are prioritized is site specific and
generally determined through stakeholder consultation (for example, between regulators,
land developers, designers and the local community). In many instances, the above
objectives are in conflict with one another, necessitating decision-makers to consider
trade-offs between objectives when assessing the performance of SWH systems.
As far as the design components of SWH systems are concerned, these include: BMPs
to capture, treat, and store raw harvested runoff; and infrastructure to further treat and
distribute harvested stormwater to end users. The BMP type and size can influence: the
volume of runoff captured for harvesting; evapotranspiration and infiltration losses, which
affect supply capacity; and pollutant control performance and harvested water quality,
which depends on BMPs operating within a preferable hydraulic loading range per unit
area that varies for different pollutants. The infrastructure required to transport treated
19 |
ADE | runoff will depend largely on site constraints and locations for balancing storage,
advanced treatment and distribution. The end use of harvested water, and its associated
risks (e.g. health, environmental), often drive decisions on the final harvested water
quality and thus the level of treatment required.
In relation to the spatial distribution of components, the optimal placement of
distributed BMPs is complex (Perez-Pedini, Limbrunner et al. 2005). BMP performance
is a function of catchment connectivity, land use type, catchment size, distance to
channels, connected impervious area, and level of pre-treatment in contributing
catchments (Perez-Pedini, Limbrunner et al. 2005, Sample and Liu 2014). BMPs at
locations closer to catchment outlets must be able to treat larger volumes of runoff
efficiently (Lee, Selvakumar et al. 2012). However, the treatment effectiveness of BMPs
can decrease with increasing inflow rates and pollutant concentrations. In addition, at sites
where limited area is available to capture, treat and store harvested water, supply capacity
can be limited (Marchi, Dandy et al. 2016). Consequently, distributing BMPs throughout
a catchment can increase treatment and storage capacity of SWH systems.
With respect to design options, for the various types of treatment BMPs, surface area
is typically the most important design parameter influencing cost and performance. The
selection of optimal BMP basin side slope, depth, and transfer infrastructure design
parameters can also be important (Marchi, Dandy et al. 2016), however, ranges for these
parameters are typically constrained based on best practice guidelines.
Given the large number of types of system components, the many different ways in
which they can be distributed spatially and the large number of available design choices,
it is difficult to identify distributed SWH designs that are optimal with respect to the
desired competing objectives. Consequently, there is a need for an integrated framework
for the conceptual design of SWH systems that considers all of the above factors in a
holistic fashion. Given the potentially large number of options, incorporation of a formal
optimization approach in such a framework is also likely to be of significant value.
However, existing studies in this field have not presented such an approach and have only
considered a subset of the above factors. For example, Sample and Heaney (2006)
considered the impact on net present value of the size and spatial distribution of integrated
infiltration basins and irrigation systems, but did not consider multiple objectives, nor a
formal optimization approach. While Browne, Breen et al. (2012) and Inamdar (2014)
20 |
ADE | considered multiple objectives in conjunction with a range of BMP alternatives for
various SWH projects within a region, they also did not utilize formal optimization
approaches, making it unlikely that the solutions that provide the best trade-offs among
objectives were identified. In contrast, Marchi, Dandy et al. (2016) did use a formal
multiobjective optimization method to design surface runoff SWH system components
(the dimensions of a wetland, detention basins, and aquifer storage transfer
infrastructure). However, they did not consider how trade-offs were influenced by a mix
of different BMP alternatives for the capture, treatment, and storage of surface runoff,
optimal locations for BMPs within a catchment, nor water quality improvement as a
formal objective. Formal optimization methods have also been used to identify the
optimal mix, size, and location of distributed BMPs (Perez-Pedini, Limbrunner et al.
2005, Maringanti, Chaubey et al. 2009, Lee, Selvakumar et al. 2012), but these studies
have not considered SWH.
To address the shortcomings in existing literature outlined above, the objectives of this
paper are:
1. to introduce a generic framework for the conceptual design of SWH systems that
considers multiple objectives, a range of BMP types and their design options, the
spatial distribution of BMPs, and a formal optimization approach for identifying
designs that represent near-globally optimal trade-offs among competing
objectives in an integrated fashion;
2. to demonstrate the application of the generic framework to a case study SWH
system for a residential development in Adelaide, South Australia; and
3. to use the case study to investigate
a. potential benefits achievable by distributing SWH components throughout
the catchment compared to systems with components only at the catchment
outlet
b. trade-offs between lifecycle cost, supply volume, and water quality
improvement, which is achieved by linking an integrated stormwater model
with a multiobjective evolutionary optimization approach, and
c. impacts of design decisions including the type, size and location of BMPs
on SWH performance.
21 |
ADE | 2.2 Proposed distributed stormwater harvesting system design
optimization framework
This section contains a description of distributed SWH systems, a mathematical
formulation of the multiobjective optimization design problem (decision variables,
objective functions and constraints) and the proposed formal optimization framework for
solving it.
2.2.1 Description of SWH systems
A spatially distributed SWH system for an urban catchment, detailed for one of
multiple sub-catchments, is illustrated in Figure 2-1. In the figure, BMPs are shown by
closed green (shaded) boxes, runoff sinks (or demands) by parallelograms, drainage paths
by solid arrows, pipe flow for treated runoff by purple (large dash) arrows, and SWH
system losses by black (small dash) arrows. After rainfall on an urban catchment, some
allotment (land parcel) roof runoff is diverted to rainwater tanks to supply water for toilet
flushing and household irrigation. Some impervious (roads, car parks) and pervious
(grassed areas, open space) surface runoff, and roof runoff overflowing or bypassing the
tank, is captured and treated in BMPs located along streetscapes or in open (green) spaces.
BMPs can include, for example, smaller biofiltration systems servicing a cluster of
allotments integrated into the streetscape or urban open space, or larger sedimentation
basins, biofiltration systems, or constructed wetlands servicing a catchment comprised of
multiple clusters. Biofiltration systems (biofilters) for SWH typically consist of a basin
overlaying a geotextile-lined filter medium with a drainage pipe at the bottom.
Sedimentation basins consist of a pond to promote settling of sediments through the
reduction of flow velocities and temporary detention. Constructed wetlands are shallow,
extensively vegetated basins that use enhanced sedimentation, fine filtration and pollutant
uptake processes to remove runoff pollutants.
After passing through a BMP, treated stormwater is typically stored at the multiple-
cluster or catchment scale in open water ponds, storage tanks, or an aquifer. Harvested
water is often transferred from sub-catchments to a central balancing tank for advanced
treatment and distribution to an irrigation network. Surface runoff that overflows or
bypasses BMPs, or is not harvested, is lost through evapotranspiration, infiltration to deep
22 |
ADE | After short-listing, often multiple BMP types and size options are available at each
location. These decision variables are denoted BMP [integer], each with associated
surface area options, denoted as SA [fraction]. SA is formulated as a fraction of the
maximum available area for a BMP at a location, denoted SA [area]. Where one BMP
max
type is available at a location, BMP is a fixed parameter, and SA is a decision variable.
Where multiple BMP types are available at a location, both BMP and SA are decision
variables. In the latter case, the surface area options depend on the type of BMP selected,
since SA , based on guidelines and site constraints, varies among BMP types. BMP
max
design parameters, such as the dimensions of basins, can be included as decision
variables. Other parameters required to model BMPs are either fixed a priori based on
design guidelines or site constraints, or dependent on the BMP surface area and calculated
once this is known. Pipes and pump configuration and parameters are selected to transfer
treated water from storage sites to central balancing storage.
2.2.2.2 Objectives
Although objectives depend on stakeholder interests, three formal objectives are
typically considered and therefore included in the proposed framework: cost, supply
volume, and water quality improvement. Cost is a key concern for decision-makers
responsible for maximising the return on investment, including capital and ongoing costs.
Maximising supply volume is a primary motivation for implementing SWH systems in
order to reliably meet irrigation demand (and contribute to runoff volume reduction).
Water quality improvement is a key environmental objective considered by regulatory
bodies (Chichakly, Bowden et al. 2013, Yang and Best 2015). As explained by Chichakly,
Bowden et al. (2013), due to their qualitative and political nature, social considerations
are taken into account through stakeholder consultation utilized when selecting available
BMP types, sizes and locations, and determining constraints, as well as when assessing
alternative candidate conceptual designs.
2.2.2.2.1 Cost
In the proposed framework, the cost of SWH concept designs is represented as a life
cycle cost LCC [$] (Equation (2-1)), which is a discounted sum of expected future costs
for stormwater management assets, including BMPs and transfer infrastructure (Taylor
and Wong 2002). The life cycle cost objective function for each candidate SWH system
is given by:
24 |
ADE | leaving the development area, and Source [mass year-1] is the mean annual mass of
pollutant that reaches the catchment outlet in a post-development catchment baseline
scenario without WSUD. Resid and Source should be determined using an integrated
stormwater model (Bach, Rauch et al. 2014).
2.2.2.3 Constraints
In the proposed optimization framework, constraints apply to conditions on types of
BMPs combined in solutions; and pollutant load reduction performance for a range of
pollutants. Each solution is assessed against conditions on the presence and size of BMPs
to avoid candidate SWH system solutions that would not be adopted in practice.
Impractical solutions can arise due to randomness in the selection of decision variables in
the optimization process (see Section 2.2.3). For example, a candidate solution might
consist of a storage device without a BMP providing inflows or a BMP may treat runoff
but not have adjacent storage where needed. Particular practical constraints need to be
agreed upon by practitioners on a case-by-case basis. In addition, many regulatory bodies
require a proportion of pollutant load generated by the development to be retained by the
SWH system to promote the health of environments receiving runoff. The proportion of
load reduction retained by the candidate SWH system is given as:
(cid:10)4KL/0L1Q ≥ (cid:10)4KL/0L1(cid:25)KST0UQ,∀ 3 = 1,...,(cid:11)(cid:3)
Equation ( 2-6 )
where, LoadRedn [fraction] is determined using Equation (2-5), LoadRednTarget
[fraction] is the mean annual proportion of pollutant load reduction target set by
regulators, c [integer] represents a target pollutant, and CN [integer] is the number of
target pollutants. As discussed by Marchi, Dandy et al. (2016), additional SWH
constraints may arise due to decision variable value ranges, land available for BMPs,
physical processes (e.g. water and energy balance), and local regulations.
2.2.3 Optimization framework
In the proposed framework, a multiobjective optimization evolutionary algorithm
(MOEA; Figure 2-2) is suggested to solve the SHW system optimization problem.
MOEAs have several advantages over traditional optimization approaches (e.g., linear
programming). They can deal with multiple objectives simultaneously (Maier, Kapelan
27 |
ADE | et al. 2014) and have been used successfully in recent planning and design optimization
studies considering SWH (Beh, Dandy et al. 2014, Paton, Dandy et al. 2014a, Marchi,
Dandy et al. 2016) and distributed BMP systems (Chichakly, Bowden et al. 2013).
Furthermore, they can be linked with multiple simulation models required to calculate
multiple objective functions and check constraints of candidate solutions (Maier, Kapelan
et al. 2014), can provide confidence in the results of the optimization process, as
simulation models that are already used in local SWH decision-making can be used
(Maier, Kapelan et al. 2014), and can enable problems with complex mathematical
properties to be considered without simplifying the optimization problem, which is not
the case when more traditional optimization approaches are used.
As part of the optimization process (Figure 2-2), a number (population) of solutions is
generated with the aid of an MOEA. Each solution represents decisions, on the type, size
and location of BMPs in a particular SWH concept design, formulated as a vector of
decision variable options. Then, solutions are ‘pre-emptively’ checked against conditions
on the configuration of BMPs. If a solution violates these conditions (i.e., is impractical),
it is not evaluated with the aid of the simulation model(s), which saves computational
time (Asadzadeh, Razavi et al. 2014). Next, the performance of practical solutions is
evaluated by calculating objective functions and checking constraints. This evaluation
requires two simulation models, including a life cycle cost model, and an integrated
stormwater model. The cost model can be a lookup table of costs associated with SWH
system components. The integrated stormwater model is needed to evaluate the
volumetric reliability and water quality improvement achieved with the distributed SWH
conceptual designs under consideration. The integrated model should be able to model:
hydrologic behaviour; pollutant generation; hydraulic and treatment behaviour of BMPs;
downstream impacts of BMPs; and water recycling through SWH. According to Bach,
Rauch et al. (2014), eWater MUSIC (eWater 2009) is the only readily available model
that includes all of these.
After evaluation, penalties are applied to objective function values of solutions that fail
to meet pollutant reduction targets. The MOEA uses objective function values to assess
the fitness of solutions and iteratively modify the population using evolutionary
processes, such as reproduction, mutation, crossover and selection. Over generations, the
population of solutions converges towards the set of Pareto optimal SWH concept
designs, which are the non-dominated designs (i.e. none of the objective functions can be
28 |
ADE | 2.3 Case study
The proposed optimization framework was applied to a SWH system design case study
for a proposed housing development consisting of 3342 allotments on 245 ha of
underutilized farmland north of Adelaide, South Australia. Figure 2-3 shows the proposed
catchment layout, including four sub-catchments. Catchment characteristics are listed in
Table 2-1. A natural creek flows to the catchment outlet at the southwest of sub-catchment
4. The footprint of flood retarding basins (proposed for the future development) were
available for multiple-cluster-scale wetlands and biofilters. South Australian regulations
require a minimum 1 kL rainwater tank per allotment.
In this study, there was no opportunity to consult stakeholders directly. Rather,
consultants who developed a SWH system for the case study site, provided planning and
design data but were not available to comment on results. Decision variable values
corresponding to BMP types and surface areas were generated using a MOEA, which
were combined with fixed and decision variable dependent parameters to form a candidate
SWH system. The objective function values were evaluated with a lookup-table cost
model and an integrated stormwater simulation model developed using the eWater
MUSIC version 6.1 software (eWater 2009). Details of the case study decision variables,
parameters, objectives, constraints, MOEA and simulation model are presented below.
30 |
ADE | options corresponding to locations within sub-catchments are summarised in Table 2-2.
BMP type (BMP [integer]) options in sub-catchments 2 and 4, where more than one BMP
type was available, included wetlands, geotextile-lined biofilters, and sediment basins
suitable for SWH in South Australia. Two locations for wetlands were available, both at
the base of retarding basins in the creek. These locations had adequate space for a wetland
inlet pond and a macrophyte zone and received sufficient inflows from multiple-clusters.
Biofilters were also available at the retarding basin footprints (as an alternative to
wetlands), and distributed at the cluster-scale. Cluster biofilters were suitable for locations
where space was limited near residential open spaces in catchments 1, 2, 3 and 4.
Table 2-2 Case study decision variables
Decision variable Sub- BMP DV Max. available
# catchment Type Type area (ha)
#
1 1 CB area 0.92
2 1 P area 0.50
3 2 CB area 0.55
4 2 SB,W, or MCB type NA
5 2 SB,W, or MCB area a
6 2 P area 1.00
7 3 CB area 0.50
8 3 P area 0.35
9 4 SB,W, or MCB type NA
10 4 SB,W, or MCB area b
11 4 P area 1.00
Note: CB = cluster-scale biofilter, P = pond; SB = sediment basin; W = wetland; and
MCB = multiple-cluster scale biofilter. NA = not applicable.
a SB = 0.869 ha; W = 1.00 ha; MCB = 0.730 ha.
b SB = 0.836 ha; W = 2.20 ha; MCB = 0.730 ha.
Open-water ponds were available to store treated stormwater at four locations within
the development site (one in each sub-catchment). The surface area (SA [fraction]) options
for BMPs were 0% (no BMP), 33.3%, 66.6%, or 100% of the available area for a location.
If a BMP size of 0% was selected by the MOEA, a sediment basin was set at multiple-
cluster-scale locations (even if a wetland or biofiltration basin was selected as the BMP
type) and a junction was set at cluster scale locations. The wetland macrophyte zone area
was limited by the space available in the retarding basin footprints. The maximum total
sizes of biofilters were limited to 1.5% of contributing impervious catchment area or
limited by site constraints, as per the relevant design guidelines (Payne, Hatt et al. 2015).
32 |
ADE | The sediment basin at each location had fixed sizes designed to accommodate peak 1 in
1-year annual recurrence interval inflows from upstream sub-catchments. Discretization
of the decision variables was selected to limit search space size due to the long run times
(approx. 12.5 seconds) required to evaluate each candidate solution with the stormwater
model.
Stormwater model inputs included fixed- and decision variable dependent- design
parameters, as follows. Wetlands had an inlet pond with surface area fixed at 15% of the
macrophyte zone area and 2 m depth. Inflows higher than those with peak 1 in 1-year
annual recurrence interval peak flows were diverted to an overflow bypass. A 48-hour
nominal detention time (residence time) was used. This is typical for SWH wetlands in
South Australia, which is a function of the wetland volume and is achieved by calculating
the corresponding nominal outlet orifice size. A 300 mm extended detention depth limited
the duration and frequency of inundation of wetland flora, but also the available detention
capacity. A 300 mm average permanent pool depth was adopted for the macrophyte zone
and was assumed to be initially full. Biofilters included biofiltration cells with a maximum
area of 800 m2 (Water by Design Australia 2015) and were modelled as a lumped single
cell for each catchment. Multiple-cluster-scale devices received inflows, diverted from
the natural creek channel, that were lower than the 1 in 1-year annual recurrence interval
peak flow rate for upstream catchments to prevent scour of the filter media. Multiple-
cluster-scale biofilters had less restrictive site constraints than cluster-scale biofilters. This
is reflected in their fixed dimensions. These are: (1) at the multiple cluster scale, 400 mm
for biofilter detention depth, 800 mm for filter depth and 400 mm for the submerged zone;
and (2) at the cluster-scale, 200 mm for biofilter detention depth, 500 mm for filter depth,
and 200 mm for the submerged zone. Both devices had 200 mm/hr hydraulic conductivity,
an underdrain with geotextile liner to maximize harvesting potential by preventing
exfiltration, and a submerged zone to promote plant health in extended dry periods and to
maximize volume retention. The interested reader is referred to Payne, Hatt et al. (2015)
and Water by Design Australia (2015) for comprehensive diagrams illustrating these
dimensions for lined biofilters. Storage ponds had 2 m total depth and 0.1 mm/hr
exfiltration rate. Extended detention depth was set to 100 mm (minimum allowable in
MUSIC) to minimize treatment modelled in the storage pond. All RWT parameters were
fixed for a 1 kL tank size. RWTs in a sub-catchment were modelled as a lumped tank
node. RWTs were connected to 100 m2 of roof area (40% of total roof area) per allotment
33 |
ADE | and supplied 50 L/day for toilet flushing. Gross pollutant traps were not modelled, as per
relevant modelling guidelines (Water By Design Australia 2010).
Cost model inputs included lifecycle cost parameters associated with BMPs in a
solution and with pipe and pump infrastructure selected to transfer water from storage
ponds to an underground balancing storage in sub-catchment 2. All transfer pipes were
assumed to be 150 mm PVC to minimise pipe velocities and head losses for the highest
demand scenario. Where a BMP was selected in sub-catchment 3 or 4, an 8 kW
submersible pump supplied 9 L/s at 60 m head to the balancing storage, as per the detailed
design adopted for the real-life SWH system (J. Cantone, personal communication, 2014).
2.3.2 Objectives
The objective function for lifecycle cost, LCC [$], was calculated using Equation (2-1)
to (2-3). The parameters for LCC [$] (Equation (2-2) were estimated from cost
harvest
schedules developed by Melbourne Water Australia (2013) and the eWater MUSIC
(eWater 2009) lifecycle costing tool (Table 2-3). A typical lifecycle period of 50 years
was adopted. A discount rate of 5.5% per year was used to calculate the present worth
factors. Although RWTs were a major cost of the SWH system ($10.7 M), this cost was
incurred in all solutions and, therefore, omitted from the life cycle cost objective function.
The parameters for LCC [$] (Equation (2-3)) were estimated as follows. Capital
transfer
costs for pipe and pump infrastructure, C [$] and C [$], were derived
CapTransPipe CapPump
from costing data for the SWH system developed for the site (J. Cantone, personal
communication, 2014; Table 2-4). The capital cost of a transfer component was included
if at least one pond requiring the component was selected by the MOEA. The net present
value (NPV) of operating costs of pipe maintenance and pumping, C [$] and C
mPipe mPump
[$], were assumed to be negligible compared to the BMP establishment and maintenance
costs, based on analysis of detailed costings for several SWH conceptual designs in
Inamdar (2014). The costs of gross pollutant traps were not included in the objective
function value since the costs applied to all solutions. Volumetric reliability (R [fraction])
V
was calculated (Equation (2-4)) using SWH model results. R was the total demand
V
supplied divided by total demand requested for the N ponds in each SWH concept design.
Total Suspended Solids (TSS) reduction was the specific pollutant constituent adopted
for the water quality objective. Maximising TSS load reduction was particularly important
since TSS limit the ability of a water body to support diversity of aquatic life, introduce
34 |
ADE | contaminants, such as heavy metals and nutrients, limit navigability and fish passage due
to sedimentation, and have undesirable aesthetic affects (Bilotta and Brazier 2008). Load
reduction (LoadRedn [fraction]; Equation (2-5)) was calculated based on catchment
TSS
outlet total TSS load divided by a baseline scenario TSS load without SWH or RWTs,
determined using the stormwater model.
Table 2-3 Breakdown of life cycle costs
Lifecycle cost components Wetland Sediment Pond Cluster Multiple-
Basin biofilter cluster
biofilter
Total Acquisition Cost 100 150 150 500 250
(TAC)($/m2) a
Annual Maintenance Cost 2 5 5 10 5
($/m2) a
Establishment Cost Factor a 2 2 2 2 2
Establishment Period 2 2 2 2 2
(years) a
Annualized Renewal cost 0.00641 × 0.0172 × 0.0172 × 0.0243 × 0.0243 ×
($/m2) b TAC TAC TAC TAC TAC
Renewal Period (years) b 25 15 25 20 25
Decommissioning cost 0.52 × 0.47 × 0.47 × 0.49 × 0.49 ×
($/m2) b TAC TAC TAC TAC TAC
Note: Annual establishment period maintenance cost = Annual maintenance cost ×
establishment cost factor. Costs are in Australian Dollars (2015$).
a Based on Melbourne Water Australia (2013).
b Based on eWater (2009).
Table 2-4 Breakdown of transfer component costs
Transfer Transfer component required? C
CapTransPipe +
component Pond 1 Pond 2 Pond 3 Pond 4 C ($ M)
CapPump
Pipe 1 Yes No No No 0.168
Pipe 2 Yes Yes No No 0.044
Pipe 3 No No Yes Yes 0.205
Pipe 4 No No Yes Yes 0.205
Pipe 5 No No Yes Yes 0.184
Pump station Yes Yes Yes Yes 0.692
2.3.3 Constraints
Solutions generated by the MOEA that violated practical constraints were allocated
extreme objective function values ($1.0 × 109 life cycle cost and 0.0% reliability), and
were not simulated. The practical constraints on BMP configuration specific to the case
35 |
ADE | pollutant load relationships based on analysis by Duncan (1999). The model SWH
drainage networks consisted of nodes representing: BMPs (and junctions at locations
where no BMP was selected by the MOEA); catchment runoff sources including roof,
ground impervious and pervious fractions of each sub-catchment; and a catchment outlet.
Nodes were connected via drainage links. The right-hand side of Figure 2-4 shows how
MUSIC models were linked with NSGA-II. Input parameters for MUSIC included: BMP
type and surface areas generated by the MOEA; catchment model parameters determined
a priori; and fixed design parameters determined a priori or calculated after the surface
areas were known. MUSIC modelled the spatial distribution of BMPs through routing
flow and pollutant transport between nodes at each time step.
2.3.6 Analyses conducted
The optimization framework was run for three demand scenarios. These were Scenario
1) low irrigation demand (61.0 ML/year), Scenario 2) high irrigation demand (for high
amenity open space; 122.0 ML/year), and Scenario 3) high demand plus 40.0 ML/year
export to a neighbouring school for non-potable use (162.0 ML/year). Annual demand
was disaggregated in proportion to potential evapotranspiration minus rainfall in each
hour for each year, using the ‘PET-rainfall’ demand function in MUSIC, as suggested in
the MUSIC guidelines. After a solution was selected by the MOEA, each storage pond
demand was allocated as follows: firstly, ponds were allocated their local sub-catchment
irrigation demand; then demand for sub-catchments without ponds was allocated to the
closest downstream pond, or the closest upstream storage pond if no downstream ponds
existed. At each time-step, demand was extracted until a water depth of 500 mm was
reached. Regional pervious surface storage parameters in the MUSIC manual (eWater
2009) calibrated for Adelaide were adopted, which is considered an appropriate approach
for MUSIC (Inamdar 2014), especially since the proposed development had a high
impervious fraction dominating runoff volumes (Dotto, Deletic et al. 2011). A one-hour
time step was adopted, since larger steps can result in harvested volume underestimation
(Coombes and Barry 2007). As recommended by Mitchell, McCarthy et al. (2008) for
SWH simulation, a series of mostly complete rainfall data over a 10-year period that
include representative long-term rainfall characteristics was selected for simulation
purposes. Consequently, data from 1990-1999 were used, as they have a mean annual
rainfall of 409 mm/year, which is close to the long-term annual average (430 mm/year).
38 |
ADE | It should be noted that this is not the case for more recent data, as South Australia
experienced a severe drought between 2001-2010. As the selected data were stationary
(unlike the more recent data), they are also suitable for perturbation for use in climate
impact studies, if desired (see Paton, Maier et al. (2013)). Flood retention, peak flow
attenuation performance, and routing were not included as these analyses are typically
carried out separately to water quality and water balance assessment using separate
simulation packages with a smaller time step, and do not form part of SWH objectives
(Water By Design Australia 2010). Flows exceeding the 1 in 1-year design volume were
diverted away from BMPs in the MUSIC model. A baseline scenario for a catchment
without SWH or rainwater tanks (i.e. only catchment runoff source nodes connected to a
catchment outlet node) was simulated in MUSIC, in order to obtain the Source (Equation
(2-5)) pollutant load values. The baseline catchment generated an annual average runoff
of 479 ML with 57,900 kg TSS, 139 kg TP, and 871 kg TN.
The NSGA-II runs had a population size of 200 with crossover and mutation
parameters of 0.9 and 0.1, respectively, and were each terminated after 100 generations.
These parameters were selected after trial-and-error runs with various parameter
combinations. NSGA-II was run eight times using different random starting seeds in
decision variable space in order to minimize the influence of the stochastic generation of
the initial population and the probabilistic effects of some of the parameters controlling
the search. Each run took approximately 45 hours on a 3.10GHz computer with 8 GB of
RAM. For each demand scenario, non-dominated solutions from the eight seed runs were
merged and the non-dominated solutions identified.
The optimization results were compared with a catchment-outlet SWH approach to
provide a benchmark comparison. The catchment-outlet approach describes a design
approach where treatment and storage BMPs are located in areas of the catchment that
receive large inflows, near the catchment outlet, which is a typical approach for designing
SWH systems in practice (Browne et al. 2012; Inamdar 2014). The catchment-outlet
conceptual designs were feasible (not necessarily optimal) solutions of the SWH problem
formulation in this paper. The catchment-outlet designs considered had a pond and
wetland or biofilter located near the catchment-outlet (sub-catchment 4), and a
sedimentation basin (sub-catchment 2). A design for each combination of BMP size
options was manually evaluated for each demand scenario using the cost model and
MUSIC. The results were sorted to identify the non-dominated catchment-outlet solutions,
39 |
ADE | which were compared with Pareto optimal solutions identified in the NSGA-II
optimization runs. All model source code, input data, and results are available (Michael,
Dandy et al. 2016a).
2.4 Results and discussion
2.4.1 Distributed versus catchment-outlet approaches
The results indicate that there is significant benefit in using the optimization
framework, since the distributed SWH system optimization results dominate the
catchment-outlet designs, except for two low-cost catchment outlet approaches that lie on
the Pareto front under scenario 3 (Figure 2-5). Distributed approaches were able to supply
more of the demand requested than the largest capacity catchment-outlet design, which
indicated space at the catchment outlet limited the harvest capacity of catchment outlet
approaches (Figure 2-5). Additionally, the catchment outlet approaches had limited
capacity to reduce TSS loads. Therefore, distributed systems achieved higher supply and
TSS reduction levels by utilizing several locations for SWH components. Optimization
results comparing distributed and catchment-outlet system performance could be used in
negotiation with stakeholders to support a distributed approach, especially where
catchment outlet space is limited.
40 |
ADE | Figure 2-5 Pareto optimal and catchment outlet solutions
2.4.2 Trade-offs in cost and volumetric reliability objectives
The cost and volumetric reliability trade-off projections in Figure 2-6. show that there
is a ‘knee’ region for each demand scenario. Moving along each front in a direction away
from the knee region, there is a diminishing return in cost or reliability, suggesting that
solutions in this region may represent a desirable trade-off between reliability and cost.
Noticeably, the knee regions occur at different levels of reliability in each demand
scenario. For example, to achieve an acceptable volumetric reliability of 80%, an
investment of $4.19 M is required for demand scenario 1 and a $9.42 M investment is
required for scenario 2; no scenario 3 solution was able to achieve a volumetric reliability
of 80% (the maximum value achieved was 76.1% at $20.6 M). For demand scenario 1,
limited returns in volumetric reliability were available away from the knee region in the
direction of increasing costs. For example, a supply reliability of 93.2% was available for
$7.52 M, whereas the maximum system reliability of 93.8% required an additional 38.7%
41 |
ADE | investment (i.e. $10.43 M). Compared to scenarios 2 and 3, the demand scenario 1 front
had noticeable discontinuities and the knee region had a smaller cost range. These were a
result of the limited number of BMPs utilized in scenario 1’s non-dominated cost-
reliability solutions, as discussed below.
2.4.3 Trends in design decisions in cost-volumetric reliability Pareto optimal
solutions
Performance and design decision values of selected solutions are given in Table 2-5
and Table 2-6. The solutions represent an extreme objective function value (solutions 1,
16, 17, 42, 43, and 77) or occur at a trade-off ‘break point’ in the objective space or design
decision space. The solutions were identified by visual inspection of the Pareto optimal
solution objective and design decision spaces. These solutions utilized multiple-cluster-
scale BMPs, as shown in the sub-catchment 2 and 4 BMP size columns in Table 2-6.
Furthermore, multiple-cluster-scale biofilters and ponds at a central location (sub-
catchment 2) and near the catchment-outlet (sub-catchment 4) were the only BMPs in all
demand scenario 1 solutions, and in low cost scenario 2 and 3 solutions, for example
solutions 17, 19, and 43. For demand scenario 1, BMPs at these locations captured
sufficient inflows and had sufficient pollutant load reduction performance to meet water
quality targets, without having to rely on cluster-scale BMPs. For demand scenarios 2 and
3, moving from low to high cost solutions, the maximum available area for BMPs at
multiple-cluster locations was utilized before additional cluster-scale BMPs. Distributed
cluster biofilters and ponds were selected more frequently in solutions with higher levels
of reliability and to meet higher demand supply volumes. These results are consistent with
sensitivity analysis of distributed BMP systems (Lee, Selvakumar et al. 2012) designed
for flow reduction and water quality improvement, which demonstrated BMPs at
locations receiving large inflows consistently appeared in Pareto optimal solutions.
Biofilters provided best return on investment for supply volume and TSS reduction, since
all Pareto optimal solutions had a biofilter in at least one location (Table 2-6). Only two,
high cost, Pareto optimal solutions had wetlands and none had a sedimentation basin.
42 |
ADE | Table 2-6 Decision variable values of selected solutions
Demand Solution # Biofilter Pond Biofilter BMP 2 SA 2 Pond 2 Biofilter Pond BMP 4 SA 4 Pond 4
scenario Cluster 1 Cluster 1 Cluster 2 (central) (central) (central) Cluster 3 Cluster 3 (outlet) (outlet) (outlet)
1 1 1 - - - B 100 33.3 - - B 33.3
3 3 - - - B 66.6 66.6 - - B 33.3
4 4 - - - B 100 33.3 - - B 33.3
7 7 - - - B 100 66.6 - - B 33.3
8 8 - - - B 66.6 66.6 - - B 66.6
16 16 - - - B 100 100 - - B 100
2 17 17 - - - B 33.3 - - - B 66.6
19 19 - - - B 33.3 - - - B 66.6
20 20 - - - B 100 66.6 - - B 33.3
27 27 - - - B 100 100 - - B 66.6
28 28 - - 33.3 B 66.6 100 - - B 66.6
29 29 33.3 100 - B 33.3 100 - - B 33.3
40 40 66.6 100 33.3 B 100 100 - - B 66.6
41 41 66.6 100 33.3 W 100 100 - - B 66.6
42 42 66.6 100 66.6 W 100 100 - - B 66.6
3 43 43 - - - B 33.3 - - - B 66.6
44 44 - - - B 100 33.3 - - B 33.3
45 45 - - - B 66.6 66.6 - - B 33.3
47 47 - - - B 66.6 100 - - B 33.3
58 58 - - - B 100 100 33.3 66.6 B 33.3
63 63 - - - B 100 100 33.3 100 B 100
64 64 33.3 100 33.3 B 100 100 - - B 33.3
77 77 66.6 100 33.3 B 100 100 66.6 100 B 33.3
Note: BMP type (BMP): B = biofilter; W = wetland. Surface area (SA); percentage of maximum available): (cid:1) = 0.0% (junction).
46 |
ADE | 2.4.5 Impact of design decisions on cost, reliability, and water quality
Figure 2-7 shows that biofilters at the central (sub-catchment 2) and outlet (sub-
catchment 4) locations (labelled as ‘BMP 2’ and ‘BMP 4’ in Table 2-6) were preferred in
most Pareto optimal solutions for scenario 1. This indicates, in addition to volumetric
reliability benefits as discussed previously, multiple-cluster-scale biofilters provided cost-
effective TSS reduction. In addition, in solutions with high TSS reduction, the central
sub-catchment 2 storage pond, and not the outlet sub-catchment 4 pond, was preferred.
The sub-catchment 2 pond contributed to the supply volume objective only and was
mandatory where the sub-catchment 2 multiple-cluster-scale biofilter was selected,
whereas pond 4 was not mandatory. Cluster-scale biofilters were selected more frequently
than other cluster BMPs in solutions with TSS reduction levels above 90%. In particular,
cluster biofilter 3 was selected frequently and provided desirable cost-TSS reduction
performance. This may be because cluster biofilter 3 treated runoff from the sub-
catchment with the highest impervious fraction (60%), which had inflows with higher
pollutant concentration and volumes than other cluster biofilters, resulting in higher
treatment efficiency, and intercepted runoff which otherwise reached the catchment-outlet
BMPs, which overflowed quickly due to the large contributing catchment and limited
capacity at the outlet.
47 |
ADE | Figure 2-7 Heat maps of Pareto optimal solution decision variable values for scenario 1
2.5 Summary and conclusions
A general multiobjective optimization framework was developed for the conceptual
design of spatially distributed stormwater harvesting (SWH) systems to address
knowledge gaps in the SWH optimization literature. The approach was applied to a case
study SWH system for a housing development north of Adelaide, South Australia. The
results demonstrate the benefits of adopting Pareto optimal spatially distributed SWH
systems identified using the framework, compared with traditional catchment-outlet
approaches. Results indicate that where storage space is limited at the catchment outlet,
in addition to better water quality improvement, better harvested stormwater supply
reliability can be achieved by distributing capture, treatment, and storage BMPs in an
integrated SWH system. In the case study, biofilters in locations with high runoff inflows
were preferred in solutions that were non-dominated with respect to all three objectives:
lifecycle cost, volumetric reliability and TSS reduction. Maximum TSS reduction was
limited primarily by available treatment BMP sizes. In addition, solutions with the highest
reliability did not coincide with those with the highest TSS reduction. This is because
although pollutant load reduction through abstraction of harvested water contributed to
48 |
ADE | improved runoff quality, major drivers for TSS reduction performance were the size and
location of BMPs. Of the cluster-scale biofilters, those strategically placed in a sub-
catchment with the highest impervious fraction that otherwise directly contributed to the
catchment outlet BMP provided the best return on investment for improvement in
reliability and TSS reduction. If decision-makers with a particular budget accepted a
slightly lower harvested water supply reliability, solutions with significantly higher TSS
reduction were available as an alternative to solutions non-dominated in cost-reliability
space.
There were several limitations to the work carried out in this study and further research
opportunities were identified. Firstly, future studies could include operating rules as
decision variables to optimize transfer and release between storage ponds, to maximize
supply volume and optimize detention storage size. Secondly, in the case study
application, MUSIC simulations were a major contributor to computer run-times.
Consequently, decision variable options were limited in order to limit the search space
and hence the number of model evaluations. This allowed convergence towards Pareto
optimal solutions in a practical time frame. Parallelization of model simulations, surrogate
modelling techniques, or additional optimization operators to prevent simulation of
inferior solutions could reduce run-time further, as discussed in Maier, Kapelan et al.
(2014). This would permit additional decision options, scenarios including the impact of
climate change on optimal BMP placement, as well as consideration of solution
robustness and uncertainty analyses.
Despite these limitations, the results presented in this study clearly show the potential
benefits provided by optimization of distributed SWH systems. As recommended by
Askarizadeh, Rippy et al. (2015), optimization frameworks, such as the one proposed in
this study, will be important decision support tools for the selection and siting of BMPs
for urban SWH into the future.
2.6 Acknowledgements
Research funding was provided by the Australian Postgraduate Award, the University
of Adelaide, and the Goyder Institute for Water Research. The authors thank Dr. Joshua
Cantone and Dr. Robin Allison for assistance with the case study data, Mr. Jeffry Newman
for assistance with software development, and Associate Professor David Rosenberg and
49 |
ADE | Abstract
Catchment management often involves the selection of a portfolio of stormwater best
management practices (BMPs) to achieve desired social, environmental and economic
benefits. However, selection of BMPs requires the optimum use of limited resources to
obtain the maximum possible benefit. In previous studies, BMP selection has either been
formulated as a multi-criteria decision analysis problem without optimization, or a formal
optimization problem with water quality and cost as objectives. However, modern BMP
technologies are designed to provide multiple catchment benefits, and decision-makers
are required to select from large numbers of combinations of BMPs whilst considering
many objectives. This study presents a formal many-objective optimization approach to
identify and select from efficient portfolios of BMPs. The optimization approach was
applied to a 4-objective case study to identify portfolios of biofilters, wetlands and swales
for a regional-scale urban catchment in a major Australian city. Visual analytics was used
to identify the trade-offs and impacts of decision options on Pareto optimal portfolio
performance. Case study results show that significant trade-offs exist between total
nitrogen reduction and cost, and between stormwater harvesting capacity and cost. This
indicates that large increases in these benefits are possible for small increments in cost by
adopting selected combinations of BMPs. Low-cost portfolios required a small number
of cost-effective ‘flagship’ projects, but had low urban greening and amenity benefits.
Portfolios that provide a desirable compromise between the four objectives were
identified by considering information from the problem objective and decision spaces.
3.1 Introduction
Sustainable integrated catchment management often involves the selection of a
portfolio of stormwater best management practices (BMPs) with precinct-sized
contributing catchments (i.e. < 1 km2) to achieve desired social, environmental and
economic benefits within a larger catchment or region (Marlow, Moglia et al. 2013).
BMPs may include structural and non-structural measures for detention, harvesting,
infiltration, evaporation, and transport of non-point urban stormwater runoff (Lerer,
Arnbjerg-Nielsen et al. 2015). Catchment managers must consider a range of performance
criteria due to several socio-political drivers including: water supply security, public
health protection, social amenity, urban flow regime improvement, environmental
54 |
ADE | protection and flood mitigation (Marlow, Moglia et al. 2013, Askarizadeh, Rippy et al.
2015). In response to these drivers, BMPs have been developed to provide multiple
functions in addition to water quality improvement, for example stormwater harvesting
(Mitchell, Deletic et al. 2007, Clark, Gonzalez et al. 2015, Di Matteo, Dandy et al. 2017)
and urban vegetation and amenity improvement (Sharma, Pezzaniti et al. 2016).
To maximize total catchment benefits for a given budget, decision-makers must select
a combination, or portfolio, of BMPs that provides the best trade-off between many
objectives. This is difficult for the following reasons (Moglia, Kinsman et al. 2012): (a)
many planning objectives need to be considered (Mitchell, Deletic et al. 2007); (b) there
are often many viable BMPs and therefore a large number of combinations of BMPs to
choose from (Maringanti, Chaubey et al. 2009); (c) identifying and representing the trade-
offs between many (more than 3) objectives can be computationally expensive and
cognitively challenging for decision-makers (Purshouse and Fleming 2007); (d) the non-
intuitive nature of multi-dimensional value analysis and unanticipated and emergent
trends can prevent decision-makers from understanding and trusting portfolio analysis
results (Fitzgerald and Ross 2015); and (e) the ability to identify the best portfolio of
BMPs is made even more difficult in practice, as often limited resources are available for
performing this task (Moglia, Kinsman et al. 2012). Therefore, to assist with selection of
suitable portfolios of BMPs to implement in a catchment management strategy, catchment
managers would benefit from a decision support approach that 1) considers numerous,
possibly conflicting, performance criteria; 2) handles a large number of decision options
and potential strategies; 3) facilitates the identification and representation of trade-offs
between performance criteria; 4) develops trusted strategies; and 5) operates within the
limits of existing planning capacities.
To enable consideration of many performance criteria, a number of multi-criteria
decision analysis (MCDA) techniques (Goicoechea, Hansen et al. 1982) have been
developed for ranking and selecting individual BMPs (Ellis, Deutsch et al. 2006, Moglia,
Kinsman et al. 2012, Jia, Yao et al. 2013), and portfolios of BMPs (Aceves and Fuamba
2016a, Aceves and Fuamba 2016b), and have been adopted in practice (Moglia, Kinsman
et al. 2012). The multi-criteria decision analysis (MCDA) approaches consider many (>3)
performance criteria but require an a priori definition of stakeholder weightings for each
criterion, or exploration within a limited region of interest, to determine ‘the most
preferred’ portfolio of BMPs or a small set of preferred portfolios for further
55 |
ADE | consideration. However, in practice decision makers often “…don't know what they want
until they know what they can get…” (Loucks 2012, Maier, Kapelan et al. 2014). This
means a change in preferences and a better understanding of the problem may occur once
a full representation of the trade-offs between the various performance criteria is
visualized and explored (Woodruff, Reed et al. 2013, Matrosov, Huskova et al. 2015).
Therefore, although MCDA approaches allow for many performance criteria to be
considered when selecting BMPs, they do not allow decision makers to understand the
full range of trade-offs for the given problem before determining their preferences, which
limits the ability to identify a suitable compromise solution. In addition, a limited number
of alternative portfolios are generated in MCDA, which limits exploration and analysis of
the influence of BMPs on the performance of portfolios that provide the best trade-offs.
Formal multiobjective optimization approaches have been developed for catchment
management problems to assist in identifying the set of BMPs that represent the best
possible trade-offs among the competing performance criteria from among the large
number of combinations possible. Recent approaches have typically included an
integrated stormwater simulation model (Bach, Rauch et al. 2014) linked with an
evolutionary algorithm for the optimal sizing and placement of BMPs (Di Matteo, Dandy
et al. 2017) within a watershed to achieve environmental benefits from treating
stormwater runoff. However, formal objectives have been limited to ecosystem health
benefits and cost for regional-scale catchment management problems (Lee, Selvakumar
et al. 2012, Chichakly, Bowden et al. 2013, Chen, Qiu et al. 2015, Zou, Riverson et al.
2015). A potential reason for this is that the number of solutions required to characterise
the Pareto front increases exponentially as objectives are added, making this process
exceptionally computationally expensive for more than two or three objectives for many
complex water resources problems (Purshouse, Deb et al. 2014). As discussed in recent
optimization studies (Kasprzyk, Reed et al. 2012, Kasprzyk, Reed et al. 2015, Matrosov,
Huskova et al. 2015, Woodruff 2016) optimizing management solutions for a sub-
problem of a many-objective problem can lead to ‘cognitive myopia’, which is a negative
decision-making bias that arises due to drawing incorrect inferences and conclusions from
limited problem information. In this light, the limited number of formal objectives in
existing studies may have encouraged solutions with sub-optimal performance with
respect to criteria that are not included as formal objectives in the optimization problem
but that are important to contemporary catchment managers (Woodruff, Reed et al. 2013).
56 |
ADE | It is therefore preferable to optimize with respect to many (relevant) formal objectives
where possible.
While it is important to consider many objectives, as well as trade-offs between them
(rather than having pre-defined weightings, as in MCDA), this makes the analysis of
many-objective optimization results difficult. This is because: (1) visualizing the trade-
offs between objectives in more than two or three dimensions can be cumbersome, (2)
many-objective Pareto fronts can have large numbers of non-dominated solutions, as the
number of Pareto optimal solutions grows exponentially with the number of formal
objectives (Hughes 2005, Chand and Wagner 2015), (3) human decision makers have a
limited cognitive load and can select between only a small number of solutions at a time
(Miller 1956), which requires techniques to reduce the Pareto frontier to a sub-set of
diverse and promising solutions to present to decision-makers (Purshouse, Deb et al.
2014), and (4) visualizing solution performance separately from decision options may
cause decision maker biases (Kasprzyk, Reed et al. 2012, Giuliani, Herman et al. 2014,
Matrosov, Huskova et al. 2015). Recently, advanced interactive visual analytics (Keim,
Andrienko et al. 2008) approaches have been applied to help humans make sense of large
and complex data sets such as many-objective optimization results (Kasprzyk, Reed et al.
2009). However, these approaches have not been applied in the catchment management
optimization literature.
In order to enable trusted catchment management strategies that are likely to be
adopted in practice to be developed within existing planning capacities, stakeholder
engagement should be encouraged in all aspects of optimization studies applied to water
resources problems (Voinov and Bousquet 2010, Maier, Kapelan et al. 2014). The
problem formulation and system models should incorporate existing practitioner
modelling practice. In addition, practitioners should aim to use optimization as a
complementary tool to existing approaches where possible. In the existing BMP
optimization literature, there is a lack of end-user input or use of problem domain
knowledge that influences optimization algorithm behaviour (Bi, Dandy et al. 2016).
Consequently, catchment management strategies developed by algorithms may not be
trusted and adopted by decision-makers who are unfamiliar with the optimization process
and who may perceive the process of selecting the Pareto set of BMP portfolios to be a
‘black box’ (Maier, Kapelan et al. 2014). In addition, integrated catchment simulation-
optimization approaches (Srivastava, Hamlett et al. 2002, Maringanti, Chaubey et al.
57 |
ADE | 2009) may not complement current practice for management of large regional urban
catchments, which typically involves ad hoc selection and implementation of BMPs as
funding becomes available. In addition, since existing data are often insufficient to
develop useful integrated catchment models at the regional scale (Bach, Rauch et al.
2014), model development may not be feasible within a limited planning time-frame and
resources. Therefore, a formal decision approach that involves stakeholders in the
selection, evaluation and analysis of portfolios of individual BMPs, but without requiring
a catchment simulation model, might encourage uptake of formal decision support
approaches by decision-makers, which would improve upon current practices.
As identified in the above discussion, catchment management decision support
approaches need to handle several objectives, consider the full trade-off space, and
develop trusted solutions based on current modelling practice. However, current
approaches have failed to meet all of these needs. While MCDA methods allow many
performance criteria to be considered when selecting a portfolio of BMPs, they require
decision-makers to define their preferences without knowledge of the full-trade-off
patterns between portfolios. Many-objective optimization approaches overcome this
limitation since they produce an approximation of the Pareto front, which allows an
exploration and analysis of a large number of portfolios to identify solutions that represent
a desirable compromise between performance criteria. However, many-objective
optimization approaches can be computationally expensive and produce a large number
of solutions to select from. In addition, simulation-optimization based approaches may
not be feasible within a catchment management authority’s planning capacities,
complementary to existing practices, nor desirable if decision-makers do not trust the
solutions developed by the optimization algorithm.
In order to address the shortcomings of existing approaches discussed above, the
objectives of this paper are: (i) to present a formal optimization approach that identifies
the best combinations of BMPs for many (> 3) objective catchment planning; (ii) to
demonstrate the utility of the approach by applying it to a case study based on an
integrated catchment management plan for a major city in Australia; and iii) to use the
case study to a) investigate the possible many-objective trade-offs between lifecycle cost,
water quality improvement, stormwater harvesting capacity and urban vegetation and
amenity improvement, b) investigate the importance of a many-objective approach
compared to a bi-objective water quality-cost optimization, as has been done in most
58 |
ADE | previous studies, c) demonstrate trends in the impact of particular BMP projects on Pareto
optimal portfolio performance, and how this may influence decision-making, and d)
identifying opportunities in the application of the framework for improving stakeholder
buy-in to optimization results.
3.2 Proposed Many-Objective Optimization Approach
This section contains a description and mathematical formulation of the multiobjective
BMP portfolio optimization problem (decision variables, objective functions and
constraints) and the proposed formal optimization framework for solving it.
3.2.1 Conceptual Outline of the Proposed BMP Selection Approach
A conceptual outline of the proposed approach to address limitations in existing
approaches to many-objective best management practice (BMP) selection for integrated
catchment management is shown in Figure 3-1. To ensure only viable and trusted BMPs
are considered, initially, a list of potential catchment management BMPs, p, is determined
by stakeholders. These BMPs are then evaluated individually by stakeholders and the
interdependencies between them determined. All possible combinations of these
individual projects make up the full portfolio solution space, which is expected to be too
large to adequately evaluate by trial-and-error or enumeration. Therefore, in order to
allow consideration of many performance criteria, F, and a wide exploration of the
potential portfolios, P, a formal optimization approach is adopted. The best combinations
of BMPs are represented as Pareto optimal solutions, P*, to a many-objective portfolio
optimization problem formulation (Cruz, Fernandez et al. 2014). In order to analyse the
large number of Pareto optimal solutions produced by the optimization process,
interactive visual analytics are used to explore trade-offs and impacts of BMPs on
portfolio performance. To ensure results are trusted and determined within limited
planning capacity, the domain knowledge of practitioners is required to evaluate the
performance of individual projects. This is also useful to identify interdependencies
between projects and to ensure appropriate constraints and interactions are incorporated
into the evaluation of portfolio objective functions. This is a pragmatic and parsimonious
alternative approach to integrated urban water simulation models that model interactions
in urban drainage, water supply and broader integrated urban water systems (Bach, Rauch
et al. 2014), but may be costly to develop for catchment management planners. The
59 |
ADE | Site characteristics are typically assessed through on-site and geospatial studies (Inamdar
2014). After site assessment, a short-list of feasible BMPs is agreed upon amongst
stakeholders taking into account the potential to achieve desired performance criteria and
other socio-political factors (Chichakly, Bowden et al. 2013, Sharma, Pezzaniti et al.
2016).
The performance of each BMP is then evaluated independently against multiple
criteria, using accepted models based on the contributing sub-watershed for each BMP,
and in consultation with experienced local experts (Inamdar 2014). In the absence of an
adequate regional-scale integrated model to evaluate the downstream impact of BMPs,
interactions (for examples of formulating interactions in portfolio optimization see (Cruz,
Fernandez et al. 2014)) between BMPs that influence individual BMP performance are
evaluated based on expert judgment and modelling of BMPs and multiple contributing
sub-watersheds, to determine decision-making rules or performance models for
interdependent projects. The individual projects, their performance, interdependencies
and practical limitations on portfolio size are then formulated as the decision variables,
objectives and constraints of a mathematical optimization problem (see Section 3.2.3).
3.2.2.2 Optimization Process
The second part of the optimization framework describes the algorithmic processes
used to solve the optimization problem. Only portfolios that are non-dominated (i.e. none
of the objective functions can be improved in value without degrading one or more of the
other objective function values) can be considered as portfolios that represent the best
trade-off between objectives. To identify the non-dominated, or ‘Pareto optimal’ solutions
to the mathematical optimization formulation a many-objective metaheuristic algorithm
is suggested as part of the optimization framework. Metaheuristic algorithms have several
advantages over traditional optimization approaches (such as linear programming). They
can deal with multiple objectives simultaneously (Maier, Kapelan et al. 2014) and have
been successful in recent planning and design optimization studies considering urban
water planning (Szemis, Maier et al. 2012, Beh, Dandy et al. 2014, Paton, Dandy et al.
2014a, Marchi, Dandy et al. 2016) and distributed BMP systems (Chichakly, Bowden et
al. 2013, Di Matteo, Dandy et al. 2017). Furthermore, they can be linked with the
evaluation models required to calculate multiple objective functions and check constraints
of candidate solutions (Maier, Kapelan et al. 2014), and can provide confidence in the
62 |
ADE | results of the optimization process, as simulation models that are already used in local
catchment planning decision-making can be used (Maier, Kapelan et al. 2014).
As part of the optimization process, a number of solutions are generated with the aid
of a many-objective metaheuristic algorithm. Each solution represents a set of binary
decisions on whether or not to adopt each available project in a portfolio. In the
construction of a solution, projects are added to a portfolio until a maximum number of
projects is reached, or all projects have been considered i.e. a portfolio can consist of
fewer than the maximum number of projects. Then, portfolios are evaluated against
logical and strategic conditions. If a portfolio violates these conditions, the objective
function values are set to a penalty value. Next, the performance of valid portfolios is
evaluated by calculating objective functions, including interactions. This evaluation
requires a model of the objective values of individual projects, and a model for each
interaction, to determine the total portfolio objective function values. After evaluation,
final penalties are applied to objective function values of solutions that fail to meet defined
constraints. The metaheuristic algorithm uses objective function values to assess the
fitness of solutions and to iteratively modify solutions. Over a number of iterations,
solutions converge towards the set of Pareto optimal portfolios, which are non-dominated
in the set of all feasible portfolios. The metaheuristic iterative approach continues until
specific termination criteria are met (for example, a maximum number of iterations). The
non-dominated solutions identified by the optimization process are Pareto optimal or near
Pareto optimal catchment management portfolios.
3.2.2.3 Visual Analysis of Pareto optimal
Portfolios
An interactive visual analytics package (Kollat and Reed 2007, Hadka, Herman et al.
2015) is suggested to assist decision makers to explore, analyse and ultimately select
appropriate portfolios that represent a desired compromise between performance criteria
and practical catchment management strategies (Maier, Kapelan et al. 2014). Firstly, the
Pareto optimal portfolio performance and decision data, as well as alternative data that
may be useful for decision-making (e.g. average contributing catchment size, BMP type,
number of projects) are uploaded into the visual analytics package. Then, high-
dimensional coordinate plots or parallel coordinate plots (Inselberg 2009) are used to
visualize the performance of the large number of Pareto optimal portfolios in many-
63 |
ADE | objective space. Then, in order to reduce the number of portfolios considered for further
analysis, dynamic filtering to eliminate undesirable solutions can be carried out by
analysts based on the decision-maker’s budget constraints and minimum preferences for
each benefit, and eliminate apparently undesirable combinations of BMPs not anticipated
a priori (Piscopo, Kasprzyk et al. 2015). Within the reduced set, decision-makers and
analysts can use brushing to highlight sub-sets of interesting solutions. Multiple linked
plots of the same data set can assist with identifying and rationalizing trade-offs, such as
conflicts and areas of diminishing returns between objectives and emergent behaviour
caused by the inclusion of particular BMPs within portfolios. Interactive visualization of
optimization objective and decision spaces simultaneously enables stakeholders, with the
assistance of analysts, to rapidly identify subsets of portfolios that contain preferred
projects and compare their performance to other portfolios. In this way, browsing through
solutions to investigate and learn about the impact of individual project preferences on
total catchment benefits can allow decision-makers to overcome institutional decision-
making biases (Kollat and Reed 2007, Matrosov, Huskova et al. 2015). Ultimately,
several desirable portfolios are selected for further consideration.
3.2.3 Optimization Problem Formulation
To identify portfolios that represent the best trade-off between many objectives, the
project portfolio selection problem is defined as the optimization of vector F(P),
composed of n objective functions:
F(P) = [f ,f ,…,f ]
1 2 n
Equation ( 3-1 )
where P is a portfolio of projects, and F is a vector of the associated costs and benefits
of a portfolio. The decision variables, objectives, and constraints particular to the
catchment management portfolio selection problem are as follows.
3.2.3.1 Decision Variables
In the framework, it is assumed that each BMP project has a pre-determined size, type
and location. As such, each decision variable is a binary variable, d, that represents the
i
decision whether or not to adopt project, p. There are N possible projects, and thus N
i p p
64 |
ADE | j
MAXIMIZE: ^e9(cid:13)b+(cid:18)f = ∑k,-&4gS30+− /0hiL+
Equation ( 3-5 )
where, [mass year-1] is the mean annual pollutant mass retained by BMPs in
each candi^de a9 t(cid:13) eb + p(cid:18)f o rtfolio, N is the number of BMPs in a portfolio, Resid [mass year-1] is
i
the mean annual mass of pollutant leaving the ith BMP’s contributing catchment area, and
Source [mass year-1] is the mean annual mass of pollutant that reaches the ith BMP’s
catchment outlet in a post-development catchment baseline scenario without intervention.
Resid and Source should be determined using a stormwater quality assessment model
accepted by the catchment management authority (Coombes, Kuczera et al. 2002, Bach,
Rauch et al. 2014).
3.2.3.2.3 Stormwater Harvesting
Average annual supply capacity (Equation (3-6)) is adopted as an indicator of
stormwater harvesting performance (Mitchell, McCarthy et al. 2008). This metric was
selected because it can be determined from generic storage-yield-reliability curves for a
catchment at the project screening phase of catchment management planning (Browne,
Breen et al. 2012, Hanson and Vogel 2014), or other techniques (Inamdar 2014). In
addition, the average annual capacity approximates the runoff volume reduction due to
harvesting, which has ecosystem health benefits (Askarizadeh, Rippy et al. 2015). The
supply stormwater harvesting objective function is:
o
MAXIMIZE: ^(cid:17)988bf = ∑k,-&gllmn+
Equation ( 3-6 )
where Supply [volume] is the average annual stormwater harvesting supply capacity
i
for the ith BMP in a portfolio, and N [integer] is the number of projects in a portfolio.
3.2.3.2.4 Urban Vegetation and Amenity Improvement
The urban vegetation and amenity improvement indicator depends on stakeholder
interests, which may include maximizing vegetation and tree coverage and quality of
recreation spaces. Each project should be appraised and evaluated (scored) by vegetation
experts. The cumulative urban vegetation improvement objective function is:
o
MAXIMIZE: ^p(cid:14)(cid:16)(cid:16)(cid:20) = ∑k,-qS001+
67 |
ADE | Equation ( 3-7 )
where Green [integer]is a score, determined by expert assessment, attributed to the ith
i
project in a portfolio.
3.2.4 Constraints
Strategic and logical constraints on the selection of projects and performance of
portfolios could be considered, and are case specific (Cruz, Fernandez et al. 2014). For
example, where multiple sub-region catchment institutions fund an integrated catchment
strategy, constraints on the selection of projects could (1) ensure equitable distribution of
projects amongst constituent catchment management sub-regions, (2) limit the maximum
number of projects in a portfolio, N , and projects within each sub-region, (3) prevent
max
the presence of mutually-exclusive projects, as some BMPs may be redundant in the same
portfolio, and (4) limit budget allocated to projects within each sub-region. Additional
considerations for portfolio-based constraints are discussed in Cruz, Fernandez et al.
(2014).
3.3 Case Study
In this study, we demonstrate the many-objective BMP selection approach on a
regional catchment management strategy for a major coastal city in Australia. A
catchment management authority (CMA) commissioned engineering consultants to
identify sites for stormwater BMPs within an integrated catchment with an outlet flowing
into a prominent marine body. The integrated catchment covers an area of approximately
700 km2, with average annual rainfall of 400-700mm, and comprised of highly urbanized
and peri-urban regions managed by three local government authorities (LGA). A primary
objective for the CMA was to reduce the nutrient load from urban stormwater runoff
flowing into the marine body. In addition, since the potential sites for BMPs were within
public open spaces managed by LGAs, stormwater harvesting for irrigation of open
spaces, increasing vegetation and public amenity value were considered important
additional benefits. The consultants identified 70 (N =70) potential biofiltration, wetlands
p
and swale projects at locations distributed in open spaces throughout the three LGA
regions. Thirteen of these have a capacity for stormwater harvesting. In addition, the
consultants agreed that a portfolio of 20 projects or fewer (N =20) was practical. The
max
BMPs were considered mutually independent, as the contributing catchment areas to each
68 |
ADE | BMP did not coincide i.e. downstream impact of BMPs would not affect the performance
of other BMPs within the large regional catchment.
The application of the proposed optimization approach was part of a real-world study
involving a multi-criteria analysis conducted to identify a portfolio of BMP projects for a
regional catchment. This allowed the authors to demonstrate how the proposed approach
can consider existing BMP selection practices, which is a study objective. As the case
study application was only intended to demonstrate the optimization approach, the results
of the study were reviewed by consultants but were not used to inform decision-making.
The names of stakeholders and catchment regions involved are not disclosed in this study
for reasons of confidentiality.
Engagement between stakeholders, engineering consultants, and the optimization
analysts (who are the authors of this study), was carried out as follows. Firstly,
engineering consultants ran one workshop where the broad catchment management
objectives were established, which was attended by a stakeholder working group, from
LGAs and the CMA, of approximately 16 people. Consultants then identified sites,
assessed them for quantitative metrics (e.g. required size of BMPs to meet water quality
constraints, cost, and stormwater harvesting capacity) and made a preliminary effort to
score each of the qualitative metrics (e.g. vegetation improvement and amenity value)
using objective thresholds. Consultants then sent these preliminary scores to LGAs and
asked to provide a response. These were generally reviewed by landscape, bushland,
horticultural and parks and open space staff. The staff involved and level of response
varied between the LGAs. Consultants then had a workshop with each of the individual
LGAs to review the sites, establish a common understanding of the whole catchment
management opportunity and confirm the proposed individual project scoring. Then,
important objectives were refined into formal optimization objectives by the consultants
and optimization analysts. The analysts used the multi-criteria evaluation data to inform
the optimization problem formulation including decision variables (projects), developing
objective functions and project objective function values, and constraints. The data used
for this study are listed in the references, tables, supplements and repository at Di Matteo,
Maier et al. (2016b).
69 |
ADE | 3.3.1 Problem Formulation
3.3.1.1 Decision Variables
The 70 potential BMPs (Table 3-1) were formulated as 70 decision points with two
corresponding decision options; to adopt or not adopt a BMP in a portfolio. Following a
preliminary desktop analysis, BMPs were determined by stakeholders to have
contributing catchments ranging in size from 3 ha to 421.2 ha, with an assumed 50%
pervious and 50% impervious area. The functional areas of BMPs were pre-determined
by consultants and sized to meet functional requirements for total nitrogen, total
phosphorous and total suspended solids runoff pollutant reduction targets (Dale Browne,
personal communication, 2016).
Table 3-1 Details of available catchment management projects
Local government Project BMP Contributing Lifecycle cost TN Reduction Total Supply Green
area (LGA) ID Type catchment area (ha) ($NPV) (kg/yr) (ML/yr) score
1 3 Biofilter 22.5 305,157 72.75 0 4
4 Biofilter 11.6 271,251 37.4 0 4
5 Biofilter 7.7 175,626 24.86 0 5
6 Biofilter 9.3 131,719 30.16 0 5
7 Biofilter 8.2 43,906 26.63 0 5
8 Biofilter 9.4 87,813 30.25 0 5
12 Biofilter 50.3 1,220,630 162.82 0 5
13 Wetland 4.8 169,532 15.49 0 5
23 Wetland 3.0 98,438 9.58 0 5
24 Wetland 13.5 459,379 43.63 0 5
25 Wetland 13.2 459,379 42.79 0 5
35 Wetland 21.5 918,757 69.5 0 5
36 Biofilter 45.2 949,379 146.3 0 5
45 Biofilter 24.8 271,251 80.17 0 7
46 Swale 64.5 123,814 208.58 0 7
50 Biofilter 9.6 187,282 31.08 11.95 6
55 Biofilter 8.7 305,157 28.27 0 8
56 Biofilter 84.9 237,345 274.58 0 5
57 Wetland 29.4 1,206,996 95.12 12.83 5
2 1 Biofilter 20.4 508,596 55.79 0 4
70 |
ADE | Equation ( 3-8 )
where Supply is the average annual supply capacity of the ith BMP in a candidate
i
portfolio of N BMPs.
Table 3-2 Cost variables for BMPs.
BMP Surface Area Construction Establishment Maintenance
(SA) (m2) Cost Cost Cost
($/m2; ($/m2/yr; ($/m2/yr;
year 0) year 1-2) year 3-25)
Wetland
0 < SA ≤ 500 150 30 10
500 < SA ≤ 10,000 100 6 2
SA > 10,000 75 1.5 0.5
Biofiltration basin
0 < SA ≤ 100 1,000 15 5
100 < SA ≤ 500 350 15 5
SA > 500 250 15 5
Swale
All sizes 35 9 3
Note: Establishment cost = Annual maintenance cost × establishment cost factor. Costs
are in Australian Dollars (2013$). Values were scaled using an inflation adjustment factor
of 1.03053 from 2013$ to 2016$.
3.3.1.2.2 Water Quality Improvement
Total Nitrogen (TN) was the specific pollutant constituent adopted for the water quality
objective. TN load reduction was particularly important since in the urban catchment it
was found by consultants that maximizing TN reduction through treatment of stormwater
also tended to reduce phosphorous, total suspended solids and other pollutants to within
target levels (Dale Browne, personal communication, 2016). The introduction of excess
anthropogenically-generated nutrients into coastal systems can cause eutrophication,
which has negative impacts. These impacts often include excessive, and sometimes toxic,
production of algal biomass, loss of important nearshore habitat, changes in marine
biodiversity and species distribution, increased sedimentation of organic particles, and
depletion of dissolved oxygen. The mean annual pollutant mass of TN retained by each
73 |
ADE | candidate portfolio ( [fraction]; Equation (3-5)) was calculated based on the sum
of average annual
TN^e m9(cid:13) ab s+(cid:18) sf
r etained by individual BMPs in a portfolio. The water quality
improvement of individual BMPs (i.e. not an integrated system of a portfolio of BMPs)
(Source - Resid ; Equation (3-5) was assessed using the integrated catchment model,
i, i
MUSIC version 6.1 (Model for Urban Stormwater Improvement Conceptualizion, eWater
(2009)), as suggested by the CMA regulations. MUSIC is an integrated stormwater model
that evaluates rainfall/runoff and pollutant generation and transport, hydraulic and
pollutant removal performance of BMPs (Bach, Rauch et al. 2014). MUSIC algorithms
simulate runoff based on models developed by Chiew and McMahon (1999) and urban
pollutant load relationships based on analysis by Duncan (1999). An assessment of
interactions between BMPs was not deemed necessary because the contributing
catchments of individual BMPs were spatially mutually exclusive.
3.3.1.2.3 Stormwater Harvesting
To determine stormwater harvesting capacity of projects, experts on stormwater
harvesting from each LGA were asked to evaluate the stormwater harvesting potential of
BMPs within their jurisdiction. They estimated the expected irrigation demand required
by open spaces near each BMP, and the average annual potential capacity to supply the
demand. The estimates were based on procedures specific to each LGA, and reflect the
stormwater harvesting objective performance values accepted by decision-makers.
3.3.1.2.4 Urban Vegetation and Amenity Improvement
The ‘green’ score’ of individual projects (which is a weighted score of several
indicators, and was developed by the authors and agreed to be used as an optimization
objective by consultants), use scores assigned by experts (see section 3.3) from each LGA
interviewed in a workshop session by consultants. The experts were asked to answer the
following questions about the BMP projects within their jurisdiction: Answer ‘Yes’ ‘No’
or ‘Maybe’ to the following questions: 1) “will native vegetation increase at the site?”, 2)
“will tree cover increase at the site?”, and, 3) “will the quality of recreation spaces in the
area increase?”. The total catchment ‘green’ score objective function was:
(cid:137)
qS001+ = (cid:135) &34S0(cid:136)
(cid:136),-
74 |
ADE | Equation ( 3-9 )
3 i^ K1h(cid:131)0S ih ′(cid:141)0h′
&34S0(cid:136) = (cid:138)2 i^ K1h(cid:131)0S ih ′(cid:1)Kn(cid:142)0′
(cid:143)
1 i^ K1h(cid:131)0S ih (cid:3)4′
Equation ( 3-10 )
where Green is the sum of scores for each project, and Score is the number of points
i j
assigned to the answer to the jth question. Since there were three questions, each project
could achieve a maximum of 9 green points, and each portfolio a theoretical maximum of
(20 × 9 = ) 180 total green points.
3.3.1.2.5 Evaluation of Individual BMPs
Before the optimization process was run, the costs and performance values of each
BMP were determined (Table 3-1). Firstly, the stormwater harvesting capacity of
individual projects was determined from LGA expert interviews. Secondly, the individual
project lifecycle costs were determined using cost parameters from Equation (3-2) to (3-4)
and (3-8) for each project. Thirdly, the water quality performance of each BMP was
determined with the aid of MUSIC. To do this, a catchment model for a 1 ha catchment
area for each LGA was developed. The model consisted of a 0.5 ha pervious catchment
node, a 0.5 ha impervious catchment node, and an outlet node to estimate the average
annual TN load per unit area of catchment with an average 50% impervious surface area
(Browne, Breen et al. 2012). One year of continuous climate data and pervious surface
parameters provided by the CMA were adopted for the catchment nodes. To estimate
Source [kg] for each BMP, the TN load from a 1 ha unit catchment area for the respective
LGA was multiplied by the contributing catchment area to each BMP in hectares. Each
BMP size was selected to remove 45% of the TN load from its contributing catchment
(i.e. Resid = (1 - 0.45) × Source), which was suggested as an acceptable performance
i i
based on advice from the consultants (D. Browne, personal communication, 2016).
Finally, Equation (3-7), (3-9) and (3-10) were applied to determine the individual project
green scores.
75 |
ADE | 3.3.1.3 Constraints
A single constraint was applied to limit portfolios to 20 or fewer projects, since more
than 20 projects was determined to be impractical to design and construct by the CMA,
as mentioned previously. The projects were assumed be independent in that the inclusion
of one project did not influence the expected benefit, cost, or feasibility of another. This
assumption was considered acceptable since the catchments contributing to each BMP
were mutually exclusive, and customers for stormwater harvesting projects could receive
supply from only one project.
3.3.2 Pareto-Ant Colony Optimization (P-ACO) Algorithm
To solve the optimization problem, a variant of the Pareto-Ant Colony Optimization
algorithm (P-ACO; (Doerner, Gutjahr et al. 2004)) metaheuristic search algorithm was
used. P-ACO was selected because it was originally developed to solve portfolio
optimization problems (Doerner, Gutjahr et al. 2004, Doerner, Gutjahr et al. 2006), has
been used successfully and adopted as a benchmark algorithm in recent three-objective
portfolio optimization applications (Cruz, Fernandez et al. 2014), and has been applied to
complex multiobjective water resources problems (Szemis, Dandy et al. 2013, Szemis,
Maier et al. 2014, Nguyen, Dandy et al. 2016). The variant adopted here, PACOA, was
demonstrated to outperform other multiobjective ant colony optimization algorithms in a
recent water resources allocation study (Szemis, Dandy et al. 2013). The algorithm
mimics the cooperative foraging behaviour of an ant species that leaves a chemical
pheromone on a ground surface. In real-life, since ants traverse short paths to food more
frequently, more pheromone is laid on short (efficient) paths. Thus, paths with higher
pheromone levels are more likely to be selected by an ant. In the algorithm, artificial ants
select between paths, which represent decisions whether or not to adopt a BMP in a
portfolio in this instance. An input template and executable for the algorithm are available
as Data Set 3 in the Supporting Information.
A summary of the steps in the PACO algorithm is shown in Figure 3-3. In the
initialization phase, the PACO search control parameters are set. The iterative process
commences where b ants are generated, each ant starting with an empty portfolio x = (0),
and the objective weights (i.e., the ant’s individual preferences) are determined randomly
for each ant. In the construction phase of the algorithm, first the order of BMPs is
76 |
ADE | randomly shuffled, to ensure BMPs are provided an equal chance of being considered first
by each ant. Then, the ant decides whether to add each BMP to a portfolio, x, by applying
a pseudo-random-proportional rule using pheromone information τ. The pheromone
i
information is stored in one 2xN matrix for each jth objective, representing the binary
options for the N possible BMPs. If the ant adds the maximum number of BMPs, N ,
max
before all BMPs have been considered, then none of the remaining BMPs are selected.
After a portfolio has been constructed, its performance is evaluated using the objective
functions (Equation (3-2) and (3-5) to (3-7)). In this case, as individual projects were
determined to be independent, the portfolio objective functions were a summation of the
constituent individual project objective function values in Table 3-1.
Figure 3-3 Portfolio optimization process for Pareto Ant Colony Optimization Algorithm
(PACOA)
After each iteration, of the b portfolios generated by the b ants, the non-dominated
portfolios are stored offline in an array. Then, as part of a global update of every element
of the j pheromone matrices, the first and second best performing solutions ranked for
each jth objective are used to apply the following equation.
(cid:136) (cid:136) (cid:136)
(cid:144)(cid:18) = (1−(cid:145))∙ (cid:144)(cid:18) +(cid:145)∙(cid:147)(cid:144)(cid:18)
77 |
ADE | 15, U i1 (cid:142)4Uℎ (cid:142)0hU K1L 21L (cid:142)0hU l4SU^4mi4
(cid:136) 10, U i1 (cid:142)0hU l4SU^4mi4
(cid:147)(cid:144)(cid:18) = (cid:148)
5, U i1 h0341L (cid:142)0hU l4SU^4mi4
0, 4Uℎ0S(cid:131)ih0
Equation ( 3-11 )
where, for each BMP, the current pheromone value for each tth binary option and jth
objective is reduced by pheromone evaporation, ρ, and increased by a pheromone value
( ). Pheromone is evaporated from decisions that are not in the best solutions for each
(cid:136)
o(cid:147)b(cid:144)je(cid:18)ctive, which makes it less likely these decisions will be selected again in future
iterations. In this way, the ant’s decision-making landscape is modified to guide ants into
regions of the search space that contain non-dominated portfolios. Since the single
constraint was handled in the construction phase, no penalty function is required for this
case study as all constructed portfolios are feasible. The interested reader is referred to
Szemis, Maier et al. (2014) for examples of objective penalty functions. The process of
developing, assessing and updating the pheromone trails to guide the PACOA to near-
optimal trade-offs continues until a specified maximum number of iterations, w, is
reached.
Before the PACOA was applied, a sensitivity analysis was conducted to identify
suitable values of parameters that control the searching behaviour of the algorithm to
maximize the likelihood the best possible approximation of the Pareto front was
generated. The ranges of parameter values tested and the final parameters selected are
given in Table 3-3.
Table 3-3 PACOA parameters tested and adopted in sensitivity analysis
PACOA Parameter Range of Values Adopted Value
Tested
Number of ants (b) 20, 200, 300,500 500
Initial pheromone (τo) 0.5, 1.0, 10.0 0.5
Evaporation rate (ρ) 0.1, 0.15, 0.2, 0.4, 0.5 0.4
Evaluations (b ×w) Up to 2,000,000 600,000
In this study, the PACO was run for 1200 iterations of 500 ants, which equates to
600,000 objective function evaluations. This number of evaluations was selected because
78 |
ADE | Figure 3-5 Parallel coordinate plot, where each portfolio is represented as a line interval
over four vertical axes indicating objective performance values. Lifecycle cost is also
represented by color to identify the cost trade-offs against each objective.
In the low-cost region, from Figure 3-4, clusters of solutions form in TN reduction-
reuse capacity space. This indicates that individual projects dominate the contribution to
total portfolio reuse capacity or total nitrogen reduction in this region. Analysis of the
BMPs comprising solutions in these clusters shows that these portfolios contain a small
number of ‘flagship’ projects with exceptionally large reuse capacity (e.g. project 61, 40
ML/year; project 67, 12.8 ML/year; project 18, 12.0 ML/year) or TN reduction (e.g.
project 48, 1152 kg/year; project 18, 1141 kg/year) appear. Portfolios containing only a
few of these flagship projects can achieve relatively high total reuse capacity or TN
capacity at relatively low cost, but also a low green score. This causes the noticeable
discontinuity in the objective space in the low-cost region, characterized by clusters of
solutions emanating from a small number of portfolios in the low-cost region in Figure
3-4 and overlapping dark blue (low-cost) line segments joining parallel axes in Figure
3-5. Moving in the preferred objective direction, adding a flagship project to create a new
portfolio on the front can cause a large increase in TN reduction or reuse capacity.
Therefore, decision-makers desiring low-cost trade-off solutions could consider
portfolios of a small number of ‘flagship’ projects, but this would considerably
82 |
ADE | compromise the urban greening and amenity performance of the catchment management
strategy.
3.4.2 Importance of a Many-Objective Problem Formulation for Catchment
Planning
The cost and total nitrogen reduction trade-off projections in Figure 3-6 show trade-
offs between water quality and cost objectives, which have been a typical formulation in
catchment management optimization studies to date. On the front, a slight ‘knee’ region
appears such that when moving along the front away from the knee region, there is a
diminishing return in these objectives. This suggests that solutions in this region may
represent a desirable trade-off between total nitrogen and cost. The trade-off pattern is
consistent with those in other catchment planning studies (Maringanti, Chaubey et al.
2009, Lee, Selvakumar et al. 2012, Chichakly, Bowden et al. 2013). However, only
considering trade-offs between water quality and cost objectives neglects the influence of
other objectives that may be important to catchment management decision makers
(Moglia, Kinsman et al. 2012). This could bias decision makers towards selection of
solutions that would lie at extremities in objective space should other formal objectives
be considered (Kollat, Reed et al. 2011).
83 |
ADE | Figure 3-6 Pareto optimal solutions identified by the optimization process projected in
water quality-cost objective space, which have been typical objectives in previous
stormwater management optimization studies. Non-dominated solutions with respect to
the two objectives are shown as solid, and approximate the best trade-off between total
nitrogen (TN) reduction and cost. Other Pareto optimal solutions in 4-objective space, but
dominated in water quality-cost space, appear transparent.
The importance of the many-objective representation of the catchment planning
problem adopted in this study is demonstrated by tracing a solution from the two-objective
knee region in Figure 3-6 through higher dimensional objective space represented in
Figure 3-7. For this purpose, Portfolio 1 (Table 3-4) is selected and marked for further
analysis because it lies at an inflection point (observed by visual inspection) in the knee
region of the two-objective trade-off front (Figure 3-7). Using the visual analytics
package, an additional harvesting capacity axis and a green score color axis are added to
create a 4-dimensional plot of the objective space (Figure 3-7). To compare Portfolio 1
with other solutions similar in cost, the analytics package’s data brushing tool is used to
highlight solutions with lifecycle costs in the range [$1.90 M, $2.70 M]. In Figure 3-7,
these solutions of interest appear opaque, and the remaining solutions that have been
84 |
ADE | ‘brushed out’ appear transparent. Portfolio 2 (Table 3-4) is selected for comparison
because although it has a 22% greater lifecycle cost and similar TN reduction compared
to Portfolio 1, it has a vastly higher reuse capacity and green score. Therefore, although
Portfolio 1 appeared in the region of best trade-off (knee region) in the lower-dimensional
TN reduction-cost representation of the objective space (Figure 3-6), it performed poorly
in reuse capacity and green score objectives. Portfolio 2 lies near but not on the non-
dominated water quality-cost front in Figure 3-7. Thus, it would not have been available
to decision makers in a bi-objective Pareto optimization approach, which has been typical
in catchment planning optimization studies to date.
When considering the project options selected in the two portfolios (Table 3-4), it is
apparent Portfolio 2 is almost identical to Portfolio 1 except for one small project (Project
38 instead of Project 33) and, importantly, two additional projects located in municipality
1 (Projects 60 and 61). Consequently, decision-makers may consider that Portfolio 2
provides a better compromise between objectives compared with Portfolio 1, due to the
reuse capacity and green score benefit the two additional projects provide.
The above results are consistent with findings in several other studies including (1) a
finding by Kollat, Reed et al. (2011) and Woodruff, Reed et al. (2013) that, generally in
optimization studies, lower dimensional problem formulations may bias selection of
solutions that would otherwise exist at low-performing extremes if additional
performance criteria were considered as formal optimization objectives, (2) a finding by
Chichakly, Bowden et al. (2013) that, for catchment planning optimization, desirable
solutions lie near but away from the two-objective non-dominated Pareto front for water
quality improvement and cost objectives, and (3) trade-offs for a stormwater harvesting
system design determined by Di Matteo, Dandy et al. (2017), which showed slight
increases in system costs could provide large increases in both water quality improvement
and harvesting capacity.
85 |
ADE | Projects in Municipality 1 - 60, 61
Projects in Municipality 2 46, 56 46, 56
Projects in Municipality 3 18, 38, 41, 48 18, 33, 41, 48
Total No. projects 6 8
3.4.3 Identifying Impacts of Project Options on Pareto Optimal Portfolio
Performance
Figure 3-8 shows combined objective performance and decision characteristics of the
Pareto optimal portfolios, which helps the analyst to overcome biases arising from
artificial distinctions between objective performance and other characteristics of the
problem (Matrosov, Huskova et al. 2015). For example, the visual interactive plot allows
the analyst to inspect which area of the trade-off front each project features in Pareto
approximate portfolios. In this way, an analyst can infer the impact of particular projects
on portfolio performance.
In Figure 3-8 (a) the opaque spheres represent portfolios containing Project 61
(lifecycle cost $381,297; TN reduction 157.92 kg/year; reuse capacity 40 ML/year; green
score 6), which was the project with the highest reuse capacity. Importantly, all portfolios
with 40 ML/year or greater reuse capacity include Project 61, and these portfolios occur
in nearly the full range of cost, TN reduction and green score of Pareto solutions.
Therefore, this indicates decision makers should probably consider Project 61 in their
final portfolio. In Figure 3-8 (b), the opaque spheres represent portfolios containing
Project 48 (lifecycle cost $915,472; TN reduction 1152 kg/year; reuse capacity 0
ML/year; green score 7), which was the project with the highest TN reduction.
Importantly, in the lower cost region, Pareto optimal portfolios with a number of smaller
solutions dominated inferior portfolios containing Project 48. This was because although
the green score of Project 48 was high (7 out of 9), the cumulative green score and/or
reuse capacity of low-cost portfolios with more projects dominated portfolios containing
a small number of projects including Project 48. This indicates multiple additional
benefits can be achieved for a similar cost by using a portfolio of projects rather than one
‘flagship’ project. In addition, decision-makers can view and assess additional (non-
objective) characteristics that may influence decision-making, for example the percentage
87 |
ADE | of the catchment treated, spatial distribution of projects throughout the catchment, or
socio-political preferences for particular projects.
Figure 3-8 Coordinate plot showing the combined Pareto optimal objectives, decisions, and
alternate data spaces. Portfolios that include, in part a) Project 61, and in part b) Project
48, are shown as opaque spheres, other portfolios are brushed out and appear transparent.
The size of spheres is proportional to the number of projects in a portfolio.
3.4.4 Improving Stakeholder Buy-In to Optimization Results
Adopting the portfolio optimization approach and involving stakeholders in the
formulation, exploration and analysis makes the decision support framework open to
stakeholder influence and complementary to existing decision analysis practices, which
can improve trust in the optimization results and increase the likelihood they will
influence final decision-making. For example, the portfolio optimization approach allows
individual BMPs to be provided by practitioners familiar with which BMPs are likely to
be technically feasible and socio-politically acceptable, which is not ensured in
simulation-optimization based BMP placement approaches (Chichakly, Bowden et al.
2013). In addition, the portfolio approach complements existing practices where MCDA
approaches are used to handle many-objective preferences to rank BMPs based on
individual or portfolio performance (Moglia, Kinsman et al. 2012), but has the advantage
that it allows trade-offs and a large number of Pareto optimal portfolios to be explored
and analysed. When formulating objective functions, stakeholders are encouraged to
consider the interdependencies between BMPs, which may result in the discovery and
deeper understanding of aspects of the problem that had not been considered previously
(Wu, Maier et al. 2016). Interactively exploring the full Pareto optimal data set enables
analysts to discover the full trade-offs between objectives, which can help decision-
makers to rationalize preferences for different benefits and may change during the
88 |
ADE | exploration process. In addition, stakeholders with a preference for particular BMPs can
explore the impact of removing portfolios containing the BMP from the Pareto set to
rapidly analyse the importance of the BMP and possible alternatives, which may help
overcome institutional biases favouring particular BMP types. In this way, exploration
may help to rationalize the benefits of a distributed stormwater harvesting and treatment
approach with a large number of BMPs over a centralized approach with high capacity
BMPs, or a mix of both (Di Matteo, Dandy et al. 2017).
3.5 Summary and Conclusion
A general multiobjective optimization framework was developed for the selection of a
portfolio of BMPs for catchment management. The framework addresses the need for a
decision support approach for the selection of BMPs that 1) considers numerous, possibly
conflicting, performance criteria, 2) handles a large number of decision options and
potential strategies, 3) facilitates the identification and representation of trade-offs
between performance criteria, which 4) develops trusted strategies, 5) within the limits of
existing planning capacities. The approach was applied to a case study catchment plan for
a catchment authority in a major coastal city in Australia. The results demonstrate the
benefits of exploring full portfolio solution trade-offs in a many-dimensional Pareto
optimal front. A comparison between the trade-off spaces of the lower dimensional water
quality-cost problem formulation, and the many-objective formulation, demonstrated that
low-objective formulations can result in Pareto optimal portfolios with low performance
in non-objective performance criteria. In this study, when stormwater harvesting and
vegetation and amenity improvement scores were included as objective functions,
solutions that were in a region of best trade-off in water quality-cost space performed
poorly in these additional objectives. The many-objective optimization results show that
sharp trade-offs exist between TN reduction and cost, and between reuse capacity and
cost, indicating small increments in cost can return large increases in both objectives.
Portfolios in the low-cost regions typically featured a small number of projects including
cost-efficient ‘flagship’ projects that provide high TN reduction or reuse capacity.
However, in order to maximize the vegetation improvement and amenity benefits,
portfolios with a larger number of lower cost BMPs distributed throughout the catchment
were preferred. Notably, the optimization formulation in the case study does not consider
interaction between having a higher harvest capacity might allow for more irrigation of
89 |
ADE | green spaces. Using the visual analytics approach to explore combined optimization and
decision spaces, the impact of individual projects that may be preferred by decision-
makers was rapidly visualized. This approach could assist in overcoming institutionally
influenced biases to include particular projects or BMP technologies to demonstrate
alternative similar cost options to decision-makers.
Future studies applying the framework could account for differences in preferences
between multiple stakeholders that may be responsible for funding over different periods
of the project lifecycle. For example, in some funding schemes, CMAs fund the capital
expenses, whereas LGAs fund the maintenance and ongoing expenses. The many-
objective problem formulation could be adapted to include specific objectives important
to LGAs, which might include individual LGA expected operating expenses, in addition
to total catchment benefits. In addition, the Pareto optimal solutions could be explored
taking into account individual objective and non-objective preferences of multiple
stakeholders. In this way, decision-makers can visualize their preferences on a trade-off
curve and compare and, through an iterative approach, visualize and negotiate acceptable
outcomes and solutions. This may be preferable to other approaches where weightings are
set a priori, which do not account for decision maker preferences in the decision space,
nor allow a visual comparison of the regions of interest preferred by several decision-
makers. Finally, the constraint for number of projects could consider the difficulty of
constructing individual BMP types (e.g., 20 swales might be easier to construct than 20
wetlands).
3.6 Acknowledgements
Research funding was provided by the Australian Postgraduate Award, the University
of Adelaide, and the Goyder Institute for Water Research. The authors thank Dr. Dale
Browne and e2DesignLab, Australia for assistance with the case study data. The data used
are listed in the references, tables, supplements and repository at Di Matteo, Maier et al.
(2016b).
90 |
ADE | Abstract
In this paper, an optimization-visual analytics framework for complex environmental
management problems involving multiple stakeholders is developed and illustrated. In the
framework, problems are represented as a series of smaller, interconnected optimization
problems, reflecting individual stakeholders’ interests. The framework uses interactive
visual analytics to explore and analyze optimization results, and Best Alternatives to a
Negotiated Alternative (BATNAs) and an approach to reframe visualizations to
encourage stakeholder negotiation. To demonstrate the utility of the framework, it is
applied to a realistic case study involving multiple stakeholder groups funding different
aspects of an integrated catchment management plan for a region of a large city in
Australia. The problem features sixteen objectives from four stakeholders. The results
indicate that the proposed framework enables the identification of solutions that provide
the best trade-offs between many objectives and provides an effective and efficient means
of assisting stakeholders with identifying acceptable compromise solutions. (147 words)
4.1 Introduction
Evolutionary algorithms (EAs) have been used successfully and extensively for
solving water resources optimization problems in a number of areas, such as engineering
design, the development of management strategies, and model calibration (Nicklow, Reed
et al. 2010, Zecchin, Simpson et al. 2012). Ultimately, EAs are intended to be used to
support decision-making through application to complex real-world problems. However,
for real-world problems, the identification of a good decision may be difficult, highly
subjective, and dependent on stakeholder values and perceptions (Maier, Kapelan et al.
2014). These issues are compounded in problems that involve multiple stakeholders, each
with their own understanding of the problem stemming from their values and priorities
placed on outcomes, costs to be borne, and responsibilities once solutions are
implemented. Therefore, in order to improve the uptake of EAs for use as decision support
tools for complex problems, there is a need to develop optimization approaches that can
handle multiple stakeholder groups, with multiple objectives for each.
As pointed out by Maier, Kapelan et al. (2014), adapting optimization approaches to
account for different stakeholder groups is difficult because: i) stakeholders have different
94 |
ADE | value sets and interests, making it difficult to arrive at a consensus on one mathematical
formulation that all stakeholders will accept, which may affect the likelihood that
stakeholders will trust the optimization process and buy-into suggested solutions, ii) the
exploration and analysis of optimization solutions requires stakeholder engagement and
expert input, iii) the non-intuitive nature of multi-dimensional value analysis and
unanticipated and emergent trends can further prevent decision-makers from
understanding and trusting optimization results, and iv) the optimization framework is
required to facilitate the identification of a final negotiated outcome and/or exploration of
resource management alternatives to be considered further.
In the past, there has been little focus on these aspects of optimization (Maier, Kapelan
et al. 2014), which largely featured studies on algorithm development, rather than
optimization approaches for decision-making support in practice. However, there has
been some progress in relation to this in recent years, including:
• The use of iterative approaches, which has allowed for multiple formulations
of the decision variables, objectives and constraints to be developed to
progressively better define optimization problems and provide an opportunity
for stakeholders to learn about the problem (Kollat and Reed 2007, Woodruff,
Reed et al. 2013, Piscopo, Kasprzyk et al. 2015, Wu, Maier et al. 2016).
• The development of an optimization framework that provides opportunities for
stakeholders to provide input into the various stages of optimization studies,
including problem definition, the optimization process, and final decision-
making (Wu, Maier et al. 2016).
• The development of many-objective optimization approaches that identify
solutions to complex problems that represent the optimal trade-off between
numerous (>3) objectives to better capture stakeholder values (Kollat, Reed et
al. 2011, Kasprzyk, Reed et al. 2012, Woodruff, Reed et al. 2013, Cruz,
Fernandez et al. 2014, Chand and Wagner 2015, Hadka, Herman et al. 2015,
Matrosov, Huskova et al. 2015, Borgomeo, Mortazavi-Naeini et al. 2016,
Woodruff 2016).
• The use of visual analytics approaches to better communicate the outputs of
optimization studies to stakeholders to help with exploration and analysis of
the trade-offs between objectives, to identify the impact of decisions on
95 |
ADE | performance, and ultimately select trusted solutions for further consideration
(Kollat and Reed 2007, Kollat, Reed et al. 2011, Woodruff, Reed et al. 2013,
Hadka, Herman et al. 2015, Matrosov, Huskova et al. 2015, Borgomeo,
Mortazavi-Naeini et al. 2016, Woodruff 2016).
These advances have made EAs more applicable to complex, real-world problems with
multiple stakeholders and many objectives. However, in previous studies, the
optimization problem to be solved has generally been represented by a single formulation,
including all decision variable options, objectives and constraints that were considered to
be relevant. This can result in the inclusion of a large number of objectives and decision
variable options, making it difficult to identify solutions that represent the best trade-offs
between objectives (i.e. the non-dominated solutions on the Pareto front, where none of
the objective functions can be improved in value without degrading one or more of the
other objective values). This is because the number of solutions required to characterise
the Pareto front increases exponentially as the number of objectives increases, thus
making this process exceptionally computationally expensive and beyond the capability
of the majority of current EAs (Cruz, Fernandez et al. 2014, Purshouse, Deb et al. 2014).
In addition, despite the recent advances in visual analytics approaches mentioned above,
the inclusion of a large (e.g. >10) number of objectives makes the identification of
solutions that provide acceptable trade-offs for different stakeholders extremely difficult,
as this can be cognitively challenging for decision-makers, particularly when dealing with
large solution sets (Purshouse and Fleming 2007).
In order to address the above difficulties, an innovative framework to identifying
stakeholder-driven, optimal compromise solutions is proposed in this paper for problems
with distinct stakeholder groups with potentially competing sets of objectives. An
example of this is the integrated management of a river system and its catchment, where
the objectives of stakeholders managing separate sub-areas of the catchment are most
likely different from each other, and different from those of stakeholders concerned with
managing the catchment as a whole. As part of the proposed framework, the overall
optimization problem is represented as a series of smaller, interconnected optimization
problems, reflecting individual stakeholders and their interests. The Pareto optimal
solutions resulting from this analysis provide the input into a collaborative, multi-
stakeholder negotiation process, as part of which visual analytics are used to identify
trusted and accepted compromise solutions. A key feature of the proposed framework is
96 |
ADE | the use of ‘best alternatives to negotiated alternative’ (BATNAs)’ as a reference point
during the collaborative negotiation process, which correspond to the solutions individual
stakeholders would implement if they were to act in isolation. This has been shown to
increase the efficiency with which negotiated compromise solutions can be achieved
(Fitzgerald and Ross 2013, Fitzgerald and Ross 2015, Fitzgerald and Ross 2016).
The objectives of this paper are: (i) to present an optimization-visualisation framework
that is geared towards the identification of negotiated compromise solutions for problems
with multiple stakeholders with distinct sets of objectives; (ii) to demonstrate the utility
of the framework by applying it to a case study based on the integrated management of a
catchment in a major city in Australia; and iii) to use the case study to a) illustrate how
the use of BATNAs can encourage the efficient identification of compromise solutions,
and b) investigate how to identify solutions that distribute benefits and costs equitably
across stakeholders.
The remainder of this paper is organized as follows. In the next section, the proposed
framework is presented. This is followed by a description of the catchment management
case study, analyses, discussion of results, and conclusions, including limitations and
future research.
4.2 Proposed multi-stakeholder optimization-visual analytics
framework
A conceptual outline of the proposed framework to addressing the limitations of
existing optimization approaches outlined in the Introduction is shown in Figure 4-1. As
can be seen, the first step involves the solution of independent, multiobjective
optimization problems for each stakeholder group in order to identify ‘best alternatives to
negotiated alternative’ (BATNAs)’ for each of these groups, which represent the solutions
each stakeholder would implement if they were to act in isolation. Knowledge of these
solutions provides a reference point for each stakeholder group during the collaborative
negotiation stage (steps 3 and 4), which is likely to increase final solution quality and the
speed with which acceptable compromise solutions between stakeholders are identified.
Identification of the solutions that are considered during the collaborative negotiation
stage occurs in steps 2 and 3. In step 2, a number of interconnected optimization problems,
97 |
ADE | one for each stakeholder, are formulated and solved, leading to the identification of joint
Pareto optimal solutions. These, and the BATNAs, are then analysed in step 3 with the
aid of visual analytics in order to identify solutions that represent suitable compromise
trade-offs between the objectives of different stakeholder groups, which are then
considered in the collaborative negotiation process (step 4) in order to arrive at an optimal
compromise solution that is acceptable to all stakeholders. Details of each of these steps
are given in the subsequent sections.
Figure 4-1 Conceptual outline of the proposed multi-stakeholder optimization-visual
analytics framework incorporating multiple problem formulations to encourage a
negotiated outcome. Steps are adapted from recommendations by Fitzgerald and Ross
(2016).
4.2.1 Selection of best alternative to negotiated agreement (BATNA)
The concept of using a BATNA for multi-stakeholder negotiation applied to
engineering systems design was developed and tested by Fitzgerald and Ross (2015)
based on principles from negotiation theory (Keeney and Raiffa 1993, Fisher, Ury et al.
2011). Fitzgerald and Ross (2015) ‘re-framed’ the visualisation of the performance of
engineering systems options about an origin defined by the performance of the BATNAs
98 |
ADE | of individual stakeholders, which improved the quality of solutions selected by
collaborating stakeholder groups, as well as the speed this was done. When used as a
reference point for alternative solutions to the problem, BATNAs defines what the
theoretical benefits and losses to stakeholders are of arriving at a compromise solution.
This improves decision-making, since humans have been shown to be more strongly
averse to decisions that result in outcomes below a reference value (losses) than they are
positive about results above the reference value (gains) (Fitzgerald and Ross 2014). There
is often some synergistic benefit to collaboration, for example through cost efficiencies
and access to more funding or a wider range of possible options and outcomes. Therefore,
setting theoretical ‘go it alone’ BATNAs as reference points highlights what is ‘lost’ by
not reaching a negotiated outcome, encouraging stakeholders to avoid the costs of not
collaborating during the exploration and analysis of alternative solutions.
As part of the proposed approach, it is suggested to identify the BATNA for each
stakeholder group with the aid of multiobjective optimization, as shown in Figure 4-1. In
this case, the formulation of the optimization problem represents a theoretical scenario
where each stakeholder develops solutions in isolation, instead of developing joint
solutions with other stakeholders in a collaborative manner. These multiobjective
optimization problems are solved using a suitable algorithm and the resulting Pareto
optimal solutions are explored and analysed using visual analytics by individual
stakeholders, with each selecting their ‘best alternative to a negotiated agreement’
(BATNA). Details of each of these steps are given in the following sub-sections.
4.2.1.1 BATNA optimization problem
formulations
To identify solutions that represent the best trade-off between many objectives for each
individual stakeholder’s ‘go it alone’ solution, a separate optimization problem is
formulated for each stakeholder as follows:
(cid:1)i1i5i(cid:150)0 "(cid:27)(cid:151):*(cid:151),(cid:17)( (cid:17)) = "(cid:27)(cid:151):*(cid:151),(cid:17) = [^(cid:152)(cid:153)(cid:154)j(cid:153)-,^(cid:152)(cid:153)(cid:154)j(cid:153)(cid:155),…,^(cid:152)(cid:153)(cid:154)j(cid:153)(cid:20)]
hg(cid:142)(cid:157)03U U4
0, i = 1, …,m
T+( ) ≤
99 |
ADE | 0, i = 1, …,p
ℎ+( ) =
Equation ( 4-1 )
where P is a set of decisions taken in isolation i.e. without collaboration by an
s
individual stakeholder, s, F is a set of the associated costs and benefits of the
BATNA
decisions, f is an objective function used to measure a cost or benefit of P under the
BATNAi
BATNA scenario, n is the number of objective functions representing the stakeholder’s
values, g is a set of inequality constraints, and h a set of equality constraints bounding the
feasible solution space. It should be noted, that each objective function used in the
BATNA problem formulation should be comparable with one of the objective functions
used in the collaborative scenario outlined in Section 4.2.2. Although the indicators of
performance of objectives might be different, the type of objectives should be consistent
for each stakeholder to allow for comparison of the optimization results between the two
scenarios.
4.2.1.2 Solving the BATNA optimization problems
Only solutions to Equation (4-1) that are Pareto optimal for an individual stakeholder
can be considered as solutions that represent the best trade-off between objectives within
each stakeholder’s problem space. It is suggested to use many-objective metaheuristic
optimization algorithms to identify these Pareto optimal points, as these algorithms have
several advantages over more traditional optimization approaches (such as linear
programming), including their ability to deal with multiple objectives simultaneously
(Maier, Kapelan et al. 2014), their successful application in recent planning and design
optimization studies (Szemis, Maier et al. 2012, Beh, Dandy et al. 2014, Paton, Dandy et
al. 2014a, Marchi, Dandy et al. 2016) and their successful linkage with many-objective
visual analytics packages (Matrosov, Huskova et al. 2015). Furthermore, they can be
linked with the models required to calculate multiple objective functions and check
constraints of candidate solutions (Maier, Kapelan et al. 2014), and can provide
confidence in the results of the optimization process, as simulation models that are already
used in stakeholder decision-making can be used (Maier, Kapelan et al. 2014).
4.2.1.3 Selecting a BATNA solution
In order to enable each stakeholder to select a BATNA solution from their Pareto
optimal solutions, use of the approach introduced by Di Matteo, Dandy et al. (2017) is
100 |
ADE | suggested. The approach uses a metaheuristic to generate optimization results, and visual
analytics to assist decision makers to explore and analyse their Pareto optimal solutions,
enabling solutions that represent an acceptable compromise to be identified. Further
details of the approach are given in Section 3.3.
4.2.2 Formulation and optimization of multiple stakeholder problem spaces
While the solutions obtained in this step still correspond to optimal alternatives from
the perspective of individual stakeholders, as was the case for the BATNAs, these
solutions are to problems that are formulated collaboratively between different
stakeholder groups, taking into account interactions and dependencies between the
problems faced by these groups, as well as any efficiencies gained. Consequently, this
step also provides an opportunity for relationship-building for stakeholders and to record
informal attributes of the problem that may assist in exploring and analysing solutions. It
is possible after collaboration commences that stakeholders find that their values align to
a degree that they form a ‘coalition’ and negotiate as one stakeholder group from a shared
position. Consequently, there may be fewer stakeholder groups undertaking the
negotiation than there were individual stakeholders assessing their BATNA.
This step consists of a number of sub-steps, including the formulation of individual
optimization problems for each stakeholder, the solution of this problem with an
appropriate multiobjective optimization algorithm and determination of the joint Pareto
front. Details of each of these steps are given in the following sub-sections.
4.2.2.1 Collaborative optimization problem
formulations
To identify solutions that represent the best trade-off between many objectives for each
stakeholder group, s´, a separate optimization problem is formulated for each stakeholder
group as follows:
(cid:1)i1i5i(cid:150)0 "(cid:17)(cid:143)( (cid:17)(cid:143)) = "(cid:17)(cid:143) = [^(cid:159)(cid:160)¡¡(cid:153)(cid:152),-,^(cid:159)(cid:160)¡¡(cid:153)(cid:152),(cid:155),…,^(cid:159)(cid:160)¡¡(cid:153)(cid:152),(cid:20)]
hg(cid:142)(cid:157)03U U4
0, i = 1, …,m
T(cid:17)(cid:143),+( ) ≤
101 |
ADE | 0, i = 1, …,p
ℎ(cid:17)(cid:143),+( ) =
Equation ( 4-2 )
where P is a set of decisions taken by a stakeholder group, F is a set of the associated
s’
costs and benefits of the decisions, f is an objective function used to measure a cost or
i,s’
benefit of P under the collaborative scenario (which should be comparable to one
objective function in the BATNA problem formulation of each individual stakeholder in
the group, see Section 4.2.2.1) n is the number of objective functions, g is a set of
,
inequality constraints, and h a set of equality constraints bounding the feasible solution
space.
During the formulation of each of the s’ optimization problems, stakeholders should
collaborate to ensure interdependencies between the benefits and costs of decisions,
available decision options and constraints are reflected in the mathematical formulations.
For each formulation, performance indicators corresponding to different objective
functions can represent the individual values of a stakeholder. However, the selected cost
indicators should enable a comparison between formulations in order to make it possible
to analyse how equitably a solution distributes costs and benefits amongst stakeholders.
For example, while the cost performance indicator could be represented as a lifecycle cost
or as separate objectives for capital and operating expenses, the corresponding indicator
should allow for consistent comparison amongst the optimization problems for the
different stakeholders. In addition, if an option selected by one stakeholder affects another
stakeholder’s available decision options or objective function value(s), then this should
be included in the decision variables of affected stakeholders.
As part of the above process, apart from the formal problem aspects, analysts should
also record the key elements of the problem structure that may be useful during later
negotiations (Fitzgerald and Ross 2016). These may include interests of stakeholders that
are divisible (for example, the possibility of sharing capital expenditure for certain
projects), or relationships between stakeholders, which can be important in informing how
the exploration and analysis should be conducted. For example, if there are known pre-
existing negative relationships between stakeholders, directly comparing desired
alternatives may limit the effectiveness of exploration and should be avoided.
102 |
ADE | 4.2.2.2 Solving the collaborative optimization
problems
As discussed in Section 4.2.1, it is proposed to use metaheuristic optimization
algorithms for the identification of the solutions that represent the best trade-offs within
each stakeholder's problem space. In the context of solving the collaborative optimization
problem, the fact that these algorithms can be linked with existing simulation models has
the additional advantage that selection of an appropriate system model can assist with
relationship-building and increase the likelihood of a negotiated outcome. This is because
models can potentially be developed amongst stakeholders through a ‘joint fact finding’
exercise to establish credible and objective data to support models; this being one of the
foundations of principled negotiation (Fitzgerald and Ross 2015). Alternatively, where
models cannot be determined through joint fact finding, stakeholders may offer existing
system models in order to promote a ‘Full, Open, and Truthful Exchange’, which is
important in successfully achieving negotiated outcomes (Fitzgerald and Ross 2015).
4.2.2.3 Determining the joint-Pareto front
Solutions that lie in all Pareto sets for the solutions to the s’ individual stakeholder
problems, that is the joint-Pareto solutions, are an obvious choice for potential
compromise solutions. This is because these solutions do not require stakeholders to
consider solutions that are not optimal for their particular problem, although changes in
their relative preferences for different objectives might be required in order to identify a
solution that satisfies all stakeholders. To determine the joint-Pareto front, firstly the
Pareto optimal solution data sets from the s’ optimization problems are aggregated. Next,
the joint Pareto front solutions, that is, solutions that lie on the Pareto front for every
stakeholder, are identified and selected. As suggested by Fitzgerald and Ross (2013), if
no joint solutions can be identified, then the Fuzzy Pareto Number (FPN) of solutions
close in objective space to the Pareto fronts for each stakeholder can be considered
(Smaling 2005, Fitzgerald and Ross 2012).
4.2.3 Visualization of the multi-stakeholder trade-off space
In the third step of the proposed framework, an analyst generates a visualisation of the
solution set on the joint-Pareto front for interactive exploration and analysis by
stakeholders so that they can ultimately select solutions that represent a desirable
103 |
ADE | compromise between performance criteria amongst the multiple representations of the
problem space (Maier, Kapelan et al. 2014). This may occur in a workshop setting or
virtually in real-time and can be done with the aid of an interactive visual analytics
package (Kollat and Reed 2007, Hadka, Herman et al. 2015), as part of which high-
dimensional coordinate plots or parallel coordinate plots (Inselberg 2009) can be used to
visualize the performance of the large number of Pareto optimal solutions in many-
objective space.
As part of the proposed framework, a separate plot is generated for each stakeholder.
These plots should be linked such that isolating or marking a solution in one plot updates
automatically on other plots. In this way, the performance of a solution can be compared
simultaneously in each stakeholder’s problem space. The individual BATNA solution of
each stakeholder should be plotted using a distinctive style (e.g. bold or coloured line) to
act as a reference point. Axes representing objective values should be oriented such that
positive outcomes point in the same direction. It should be noted that in parallel coordinate
plots, if the positive direction is at the top of the axis, the solutions with all objective
values above (or equal to) the BATNA represent an improvement on the reference point.
In visualisation of trade-offs between many-objectives using multiple axes, it is
possible that solutions improve upon the BATNA in one benefit but not others. For
solutions with these characteristics, whether the BATNA is superior depends on
stakeholder preferences. Therefore, an indicator of the performance of solutions relative
to the BATNA should also be visualised within each stakeholder’s problem space. This
allows stakeholders to rapidly detect how a solution performs relative to their own
BATNA and the BATNAs of other stakeholders by inspecting the multiple problem space
visualisations. An example of possible categories for a problem formulation with four
objectives – one cost, three benefits – is shown in Table 4-1. In the example, Category 1
solutions are obviously superior to those in Category 8. However, when choosing amongst
Category 2-7 solutions, stakeholder input is necessary, as improvements or losses in one
benefit might be valued more highly than those in others. In addition to visualising the
category of solutions, automated preference selection techniques might further assist with
selecting between solutions and reducing the size of a large solution set (Fitzgerald and
Ross 2016).
104 |
ADE | Table 4-1 Categories of solutions indicating performance relative to BATNA
Category Lower cost than Number of benefits
BATNA? exceeding BATNA
1 Yes 3
2 Yes 2
3 Yes 1
4 No 3
5 Yes 0
6 No 2
7 No 1
8 No 0
4.2.4 Exploration of the multi-stakeholder trade-off spaces
In the fourth step of the proposed framework, an analyst guides stakeholders through
an exploration and analysis of the solution set. A method to do this is adapted from steps
for a multi-stakeholder trade-off space analysis suggested by Ross, McManus et al.
(2010), as outlined below.
4.2.4.1 Each stakeholder selects several ‘good’
solutions
Firstly, several good solutions are selected by individual stakeholders, only
considering the performance of joint-Pareto solutions in their own problem space (i.e. the
problem spaces of other stakeholders are hidden). To do this, the stakeholder can use a
visual analytics method to isolate promising solutions. For example, in order to reduce
the number of solutions considered for further analysis, dynamic filtering to eliminate
undesirable solutions can be carried out by an analysts based on the decision-maker’s
budget constraints and minimum preferences for each benefit. This process will eliminate
apparently undesirable combinations of decision options not anticipated when
formulating the problem (Piscopo, Kasprzyk et al. 2015). Within the reduced set,
decision-makers and analysts can use brushing to highlight sub-sets of interesting
solutions. Multiple linked plots of the same data set can assist with identifying and
105 |
ADE | rationalizing trade-offs, such as conflicts and areas of diminishing returns between
objectives and emergent behaviour influenced by the selection of various decision
options. Interactive visualization of optimization objective and decision spaces
simultaneously enables stakeholders, with the assistance of analysts, to rapidly identify
subsets of solutions that contain preferred decisions and compare their performance to
that of other solutions. In this way, browsing through solutions to investigate and learn
about the impact of individual decision preferences can allow decision-makers to
overcome institutional decision-making biases (Kollat and Reed 2007, Matrosov,
Huskova et al. 2015). Ultimately, several desirable solutions are selected for further
consideration.
4.2.4.2 Stakeholders share their preferred
solutions
Stakeholders then share their selected solutions and visualise the selected solutions of
others in their problem space. Stakeholders can record which solutions they will consider
further. Negotiations and compromises in preferences commence. As an indicator of
solution performance that can be compared among stakeholders, the solution category
relative to the BATNA can drive negotiation for compromise in preferences of
stakeholders whose solutions are more favourable. Stakeholders may express which
objectives they are willing to compromise in, and can set minimum limits on particular
benefits using brushing tools, that hide solutions that do not meet their minimum
performance criteria on other stakeholders’ problem spaces. The many-objective plots
show explicit trade-offs in each objective, and stakeholders can make judgements on the
benefits lost or gained when opting for one solution over another. Compromises can be
expressed through negotiation, which makes explicit what is being compromised and
traded.
4.2.4.3 Negotiate and identify compromise
solutions
Advanced techniques for eliminating solutions through relaxation of value constraints
and cost bargaining can be undertaken to isolate one or two solutions for further analysis
(Fitzgerald and Ross 2013). If stakeholders determined they are indifferent to the values
a particular objective takes, they may remove that objective from the visualisation of the
106 |
ADE | problem space. Omitting one objective may reduce the number of solutions in the joint-
Pareto set. If the visualisation dataset is linked to the full set of optimization results, a new
Pareto sort on the remaining objectives will eliminate solutions dominated in the lower-
objective space. As a compromise for removing an objective, stakeholders might increase
their minimum acceptable benefit on other objectives. For minimum performance
constraints on objectives that eliminate a large number of solutions, a stakeholder might
consider accepting a lower benefit in exchange for lowering the maximum cost to
contribute to a solution. In addition, cost bargaining might be undertaken amongst
stakeholders, especially where slight increases in cost for one stakeholder make available
solutions that create much higher benefits for others. Ultimately, one or two acceptable
compromise solutions should be determined for further consideration.
4.2.4.4 Explore better compromise solutions
Once acceptable compromise solutions have been identified, stakeholders search the
full set of joint-Pareto solutions for comparable solutions that are ‘fairer’. These are
identified by negotiation. The compromise solutions are plotted with an identifying
marker. To compare the solution set to the compromise solutions, an additional indicator
that measures the distance in objective space from the solution for each stakeholder
problem can be determined. An additional plot with axes of equity indicators and/or a
breakdown of the distribution of costs can be used to identify solutions that improve on
the compromise.
4.2.4.5 Further consider selected solutions
Finally, solution(s) that are acceptable to all stakeholders may be explored and tested in
more depth e.g. for robustness or other metrics (Herman, Reed et al. 2015, Giuliani and
Castelletti 2016, Maier, Guillaume et al. 2016), and a final solution selected.
4.3 Case study
The proposed framework was demonstrated on a case study for an urban catchment
management problem in Australia, which expands upon the case study originally
formulated in Section 3.3. The problem involved four stakeholders. A catchment
management authority (CMA) was responsible for funding the capital expenses of
107 |
ADE | stormwater control systems distributed throughout a catchment. Three local government
authorities (LGAs) managed regions within the catchment and were responsible for
maintenance to ensure systems remain functional over their design life. It should be noted
that there was no stakeholder involvement in the application of the proposed framework
to the case study, which was undertaken solely by the analyst for the sake of illustrating
the approach. However, although stakeholders were not involved directly in this exercise,
the generic preferences and motivations of stakeholders were discussed between the
analyst and engineering consultants who had interviewed stakeholder groups in
workshops related to the problem under consideration.
The application of the proposed optimization approach was part of a real-world study
involving a multi-criteria analysis conducted to identify a portfolio of BMP projects for a
regional catchment. This allowed the authors to demonstrate how the proposed approach
can consider existing BMP selection practices, which is a study objective. As the case
study application was only intended to demonstrate the optimization approach, the results
of the study were reviewed by consultants but were not used to inform decision-making.
The names of stakeholders and catchment regions involved are not disclosed in this study
Engagement between stakeholders, engineering consultants, and the optimization
analysts (who are the authors of this study), was carried out as follows. Firstly,
engineering consultants ran one workshop where the broad catchment management
objectives were established, which was attended by a stakeholder working group, from
LGAs and the CMA, of approximately 16 people. Consultants then identified sites,
assessed them for quantitative metrics (e.g. required size of BMPs to meet water quality
constraints, cost, and stormwater harvesting capacity) and made a preliminary effort to
score each of the qualitative metrics (e.g. vegetation improvement and amenity value)
using objective thresholds. Consultants then sent these preliminary scores to LGAs and
asked to provide a response. These were generally reviewed by landscape, bushland,
horticultural and parks and open space staff. The staff involved and level of response
varied between the LGAs. Consultants then had a workshop with each of the individual
LGAs to review the sites, establish a common understanding of the whole catchment
management opportunity and confirm the proposed individual project scoring. Then,
important objectives were refined into formal optimization objectives by the consultants
and optimization analysts. The analysts used the multi-criteria evaluation data to inform
the optimization problem formulation including decision variables (projects), developing
108 |
ADE | objective functions and project objective function values, and constraints.. The data used
for this study are listed in the references, tables, supplements and repository at Di Matteo,
Maier et al. (2016b).
4.3.1 Background
4.3.1.1 Catchment management problem
considered
Sustainable integrated catchment management often involves the selection of a
portfolio of stormwater best management practices (BMPs) with precinct-sized
contributing catchments (i.e. < 1 km2) to achieve desired social, environmental and
economic benefits within a larger catchment or region (Marlow, Moglia et al. 2013).
BMPs may include structural and non-structural measures for treatment, detention,
harvesting, infiltration, evaporation, and transport of non-point urban stormwater runoff
(Lerer, Arnbjerg-Nielsen et al. 2015). Catchment managers must consider a range of
performance criteria due to several socio-political drivers, including: water supply
security, public health protection, social amenity, urban flow regime improvement,
environmental protection and flood mitigation (Marlow, Moglia et al. 2013, Askarizadeh,
Rippy et al. 2015). In response to these drivers, BMPs have been developed to provide
multiple functions in addition to water quality improvement, such as stormwater
harvesting (Mitchell, Deletic et al. 2007, Clark, Gonzalez et al. 2015, Di Matteo, Dandy
et al. 2017) and urban vegetation and amenity improvement (Sharma, Pezzaniti et al.
2016). To maximize total catchment benefits for a given budget, decision-makers must
select a combination, or portfolio, of BMPs that provides the best trade-off between many
objectives. Selection of a portfolio of BMPs is made more difficult in practice, as often
limited resources are available for performing this task (Moglia, Kinsman et al. 2012).
4.3.1.2 Multi-stakeholder aspects of the problem
In recent years, millions of dollars have been invested into stormwater treatment best
management practices (BMPs) in Australia to improve urban ecosystem health. The
investment strategy may involve an integrated catchment approach, where a catchment
authority subsidises construction and establishment of distributed BMPs to be operated
109 |
ADE | 4.3.2 Selection of best alternative to negotiated agreement (BATNA)
For the sake of demonstrating the proposed approach, BATNAs were selected by
analysts based on a ‘build alone’ scenario, where each stakeholder is responsible for the
capital and operating costs (total lifecycle costs) of the projects they select. The optimal
solutions were identified with the aid of the general multiobjective optimization
framework introduced in Section 3.2, as this was developed for the selection of a portfolio
of BMPs for catchment management, as is the case here. The formulation of the
optimization problem is detailed in Section 4.3.2.1, details of the objective functions and
how they were evaluated are given in Section 4.3.2.2 and the specifics of the optimization
engine used are provided in Section 4.3.2.3.
4.3.2.1 BATNA optimization problem
formulations
Details of the optimization problem formulations for obtaining the BATNAs for each
of the four stakeholders are given in Table 4-2. As can be seen, LGA stakeholder
portfolios consisted of up to 7 projects located within their jurisdictions. The catchment
management authority was assumed to have permission to build and operate up to a total
of 20 projects should no agreement to share capital and operating costs be negotiated.
Table 4-2 Optimization problem formulations for stakeholder best alternative to
negotiated agreement (BATNA)
Formulation Stakeholder Decision Objectives Constraints
problem space variables (F )
BATNA
1 Catchment All projects LCC, ≤ 20 projects
CMA
management f ,
qualityCMA
authority (CMA)1 f ,
SWH CMA
f ,
Green CMA
2 LGA 1 LGA 1 LCC, ≤ 7 projects
1
projects f ,
quality1
f ,
SWH1
f ,
Green 1
3 LGA 2 LGA 2 LCC, ≤ 7 projects
2
projects f ,
quality2
f ,
SWH2
f ,
Green 2
111 |
ADE | 4.3.2.3 Optimization algorithm and analyses
As mentioned previously, the above multiobjective optimization problem formulations
for each of the four stakeholders were solved using the many-objective portfolio
optimization approach in Section 3.2. The approach uses a metaheuristic algorithm, the
Pareto Ant Colony Optimization Algorithm (PACO), which was previously demonstrated
successfully for the single stakeholder case study version of the catchment management
problem, also in Section 3.3. The algorithm mimics the cooperative foraging behaviour
of an ant species that leaves a chemical pheromone on a ground surface. In real life, since
ants traverse short paths to food more frequently, more pheromone is laid on short
(efficient) paths. Thus, paths with higher pheromone levels are more likely to be selected
by an ant. In the algorithm, artificial ants select between paths, which represent decisions
whether or not to adopt a BMP in a portfolio in this instance, with paths that result in
better objective function values receiving more pheromone.
The steps in the PACO algorithm are shown in Figure 4-2. In the initialization phase,
the PACO search control parameters are set. The iterative process commences where b
ants are generated, each ant starting with an empty portfolio x = (0), and the objective
weights (i.e., the ant’s individual preferences) are determined randomly for each ant. In
the construction phase of the algorithm, first the order of BMPs is randomly shuffled, to
ensure that all BMPs are provided an equal chance of being considered early on by each
ant. Then, the ant decides whether to add each BMP to a portfolio, x, by applying a
pseudo-random-proportional rule using pheromone information, τ. The pheromone
i
information is stored in one 2xN matrix for each jth objective, representing the binary
options for the N possible BMPs. If the ant adds the maximum number of BMPs, N ,
max
before all BMPs have been considered, then none of the remaining BMPs are selected.
After a portfolio has been constructed, its performance is evaluated using the objective
functions (Equation (D-2) and (D-5) to (D-7)). In this case, as individual projects were
determined to be independent, the portfolio objective functions were a summation of the
constituent individual project objective function values in Table D-1.
113 |
ADE | case study as all constructed portfolios are feasible. The process of developing, assessing
and updating the pheromone trails to guide the PACOA to near-optimal trade-offs
continues until a specified maximum number of iterations, w, is reached.
Before the PACOA was applied, a sensitivity analysis was conducted to identify
suitable values of parameters that control the searching behaviour of the algorithm to
maximize the likelihood the best possible approximation of the Pareto front was
generated. The sensitivity analysis was applied to one stakeholder problem formulation,
formulation 1, which is the CMA’s BATNA scenario formulation. The results of
formulation 1 were explored in depth in Section 3.3. The ranges of parameter values tested
and the final parameters selected for all formulations (i.e. formulations 1-8 in this study)
are given in Table 4-3.
Table 4-3 PACOA parameters tested and adopted in sensitivity analysis
PACOA Parameter Range of Values Adopted Value
Tested
Number of ants (b) 20, 200, 300,500 500
Initial pheromone (τ ) 0.5, 1.0, 10.0 0.5
o
Evaporation rate (ρ) 0.1, 0.15, 0.2, 0.4, 0.5 0.4
Evaluations (b ×w) Up to 2,000,000 600,000
In this study, as in Section 3.3.2, the PACO was run for 1200 iterations of 500 ants,
which equates to 600,000 objective function evaluations. This number of evaluations was
selected because there were no further meaningful changes in the Pareto front (assessed
by visually inspecting the Pareto optimal solution set at 5,000 evaluation intervals) after
this number of evaluations in a trial run of 2,000,000 evaluations. The optimization results
were re-run 50 times using different random starting seeds for the pseudo-random number
generator used in the algorithm to minimize the impact of probabilistic effects of some of
the operators that influence the search. Each run took approximately 26 minutes on a
3.10GHz computer with 8 GB of RAM, although multiple instances were run on one
machine simultaneously. The Pareto optimal solutions for each stakeholder shown in this
paper are the result of a non-dominated sort of the solutions from the 50 replicate runs.
Once the Pareto set of portfolios was determined, a suitable BATNA portfolio was
selected for each stakeholder, as detailed in Section 4.4.1.
115 |
ADE | 4.3.3 Formulation and optimization of multiple stakeholder problem spaces
The overall process used to identify the solutions that provide the input into the
collaborative, multi-stakeholder negotiation process is identical to that used to identify
the BATNAs in that individual optimization problem formulations are developed for each
of the four stakeholders, which are solved using the many-objective portfolio optimization
approach in Section 3.2. However, the formulations of the optimization problems were
altered to reflect the proposed shared funding scheme in the collaborative scenario, as
shown in Table 4-4. These formulations reflect the proposed strategy where the CMA
funds capital costs and the LGAs fund ongoing costs of projects.
Table 4-4 Optimization problem formulations for stakeholder negotiations
Formulation Stakeholder Decision Objectives Constraints
problem space variables (f ´)
COLLAB
5 Catchment All projects CAPEX , ≤ 20 projects
CMA
management f , ,
qualityCMA
authority f , ,
SWH CMA
(CMA) f ,
Green CMA
6 LGA 1 LGA 1 OPEX , ≤ 7 projects
1
projects f , ,
quality1
f , ,
SWH1
f ,
Green 1
7 LGA 2 LGA 2 OPEX ≤ 7 projects
2
projects f , ,
quality2
f , ,
SWH2
f ,
Green 2
8 LGA 3 LGA 3 OPEX , ≤ 7 projects
3
projects f , ,
quality3
f , ,
SWH3
f ,
Green 3
The objective functions for total nitrogen reduction, stormwater harvesting, and urban
vegetation and amenity improvement used were identical to those used for the BATNA
formulations (see. Equation (D-4) to (D-8)). This means that the values of f , f ,
quality SWH
f are simply the sum of the values for the LGAs. However, the cost objective functions
Green
were revised for the stakeholder collaboration problem as the CMA funded capital costs
116 |
ADE | and solution type (on the BATNA axis: BATNA = 1, Pareto optimal = 2). The colour of
the line segment indicated whether the solution has lower or higher cost and benefits
compared with the BATNA. A blue line segment indicated the most desirable (Category
1) solutions, which has all three benefits higher, and a lower cost than the BATNA of the
stakeholder. A red line segment indicated the least desirable (Category 8) solutions, which
have all three benefits lower, and a higher cost than the BATNA. Other colours represent
categories that have a combination of benefits improved and not improved, and higher or
lower costs, compared to the BATNA, as described in Table 4-1. It should be noted that
the category indicator should not be used as an absolute indicator of preference, as it does
not take into account which of the benefits is compromised. It may be desirable to
compromise on some objectives and not others, which is dependent on stakeholder
preferences.
Visualising the solution categories with colour for all stakeholders simultaneously
allows analysts and stakeholders to inspect the performance of negotiated solutions
compared to what they would otherwise achieve (i.e. relative to the BATNA). As the
benefits/consequences of a negotiated outcome for all stakeholders are visualised, framing
the solution space in this way can encourage stakeholders to continue to engage in
negotiations until a compromise is found and to ‘buy into’ the negotiated outcome.
4.3.5 Exploration of the multi-stakeholder trade-off spaces
To demonstrate the proposed framework, an analyst performed the task of stakeholders
selecting solutions from the collaborative problem formulation optimization results and
analysing them with respect to the individual stakeholder spaces. Stakeholders were not
available, and also a workshop setting with multiple participants was outside the scope of
this study. Instead, this study aimed to include tested technologies (i.e. interactive visual
analytics, and approaches in multi-stakeholder tradespace analysis) into a novel
framework to solve many-objective optimization problems. First, ‘good’ solutions were
selected for each stakeholder from the joint Pareto set. Using interactive visualisation, a
small number of solutions preferred by each stakeholder was selected individually, and
shown in the trade-off space of other stakeholders to visualise their performance. To do
this, using the visual analytics package, the analyst identified one or two solutions that
each stakeholder would be comfortable with as the negotiated outcome. The process for
selecting these solutions was like the selection of the BATNA, except the trade-off space
119 |
ADE | consists of the joint-Pareto front solutions. The solutions were then visualised in the multi-
stakeholder trade-off space to determine how solutions selected for individual
stakeholders perform for all other stakeholders. Finally, for each stakeholder, each
solution was analysed against the performance of the preferred solution and BATNA of
that stakeholder, and suggested reasoning for whether the stakeholder would accept,
maybe accept or not accept the solution were recorded in a table.
4.4 Results and discussion
4.4.1 Identifying Best Alternatives to Negotiated Agreement (BATNAs)
The outcome of the multiobjective optimization process of the ‘stand-alone’
formulations developed for each of the four stakeholders (Section 4.3.2) is a parallel
coordinate plot for each stakeholder, where each line corresponds to a Pareto optimal
solution, as illustrated in Figure 4-3 for one of the LGAs. The plots are linked via a data
set, in that manipulations (e.g. brushing out solutions) in one plot are updated immediately
on all others. In order to determine the BATNA from these solutions, the following
process was used.
For each LGA, firstly the lifecycle cost budget was limited by constraining the
assumed capital expenditure (CAPEX) available for portfolios using a brushing tool on
the interactive plot in order to reduce the number of solutions from which to select the
BATNA. Although not a formal objective, CAPEX was selected as a limiting constraint,
as it was assumed LGAs had limited funds available to spend on projects in the short-
term. Next, solutions that provided a desirable trade-off between stormwater harvesting
and green score (with TN reduction as a less influential objective for LGAs) were
selected. This was done by gradually increasing the minimum allowable green score or
SWH until two solutions with equal performance in these objectives remained. The
solution with the highest TN reduction was then selected as the BATNA, as shown by the
dark blue solution in Figure 4-3. For the catchment management authority (CMA), the
portfolio that maximized TN reduction after the solution space was constrained to a
lifecycle cost budget of $5 million was assumed. The BATNAs for each stakeholder
resulting from the above process are shown in Table 4-5.
120 |
ADE | of solutions. As can be seen, the LGA stakeholders have a large number of solutions in
Category 1 (blue), which indicates negotiated solutions will provide them additional
benefit for all objectives at lower cost compared with the BATNA. This is because the
BATNA requires individual LGAs to fund both OPEX and CAPEX of their projects,
whereas the CMA funds CAPEX in a negotiated solution. Therefore, disregarding
external factors impacting decision-making, all LGAs have an incentive to arrive at a
negotiated solution. Although individual solutions may lie in Category 1 for some, but
not other, LGAs, visualising the trade-off space in his way can remind stakeholders that
improvements on the BATNA are possible, which may facilitate negotiation.
The CMA, however, does not have any solutions in Category 1, which means it must
compromise on at least one benefit achieved by the BATNA and/or opt for a higher cost
solution. Although Category 1 solutions were featured in the CMA’s full trade-off space
of 2535 solutions, the joint-Pareto front solutions were not among these. Since the CMA
must compromise in at least one benefit to improve on its BATNA for an equal or lower
cost, it could suggest ways to arrive at a compromise with other stakeholders. For
example, the CMA could indicate to stakeholders it will only accept a solution that
provides much higher benefit in one of its primary objectives (e.g. reducing TN load to
the bay). Alternatively, it may request additional contributions from the LGAs towards
the CAPEX.
122 |
ADE | 4.4.3 Exploring the multi-stakeholder trade-off spaces
The results of an analyst exploring the individual stakeholder problem spaces to select
‘good’ individual options, presenting those options in a visualization intended to illustrate
their distribution of costs and benefits amongst stakeholders, and analysis of the solutions
in the individual trade-off space of stakeholders, as described in Section 4.3.5, are
presented in this section.
4.4.3.1 Selecting ‘good’ solutions
For the case study considered, individual LGA and CMA solutions were selected by
an analyst using parallel coordinate plots of stakeholder objectives, as stakeholders were
not available, as mentioned previously. To select LGA solutions, only Category 1
solutions were considered. Two solutions were selected for each LGA, one from high-
cost and one from low-cost Category 1 solutions. Stormwater harvesting capacity and
green score were prioritised over total nitrogen removal for solutions proximate in the
cost regions. To select CMA solutions, Category 2, 3 and solutions that exceeded the
BATNA’s TN removal with cost less than $6M, were considered. Two CMA solutions
were selected, one high cost and one low cost. The selected solutions are shown in Table
4-6.
124 |
ADE | 4.4.3.2 Sharing preferred solutions
Figure 4-5 shows the parallel coordinate plot used to identify solutions that are a
compromise between stakeholder preferences. Axes show the CMA capital expenditure
breakdown by LGA, and solution equity indicators relevant to the problem. In this case,
solutions that are likely to be preferred by stakeholders should distribute CAPEX funding
amongst stakeholders fairly whilst ensuring return on investment through total catchment
benefits are achieved. Visualising how a solution distributes costs and benefits amongst
stakeholders can assist in the negotiation process. This can be done by visualising
objective performance (CAPEX), non-objective data (CAPEX of LGAs), as well as equity
indicators (maximum BATNA category) in parallel coordinate plots. The interactive plots
allow analysts to rapidly brush out unfavourable solutions. This reduces the number of
solutions to consider and thus the cognitive load on stakeholders.
In addition, Figure 4-5 shows how CAPEX from the CMA is distributed amongst
LGAs for the selected solutions. Although the CAPEX here is more than the CMA’s
BATNA cost, the CMA may investigate higher cost solutions, as it had no Category 1
solutions in the joint Pareto front. This could result in the avoidance of solutions that have
extremely low or high individual LGA CAPEX expenditures. Since the CMA is
compromising its preferences by increasing its CAPEX over its BATNA cost, it would
most likely want to maximize its primary objective, which is to reduce total nitrogen
reduction to the bay. The ‘maximum category’ axis is an equity indicator that assumes
that a smaller number of categories is preferable. However, which of the benefits are
compromised is important to decision makers. For example, the CMA may be willing to
accept a higher category solution (e.g. higher cost and compromise in one or more
benefits) that has a much higher total catchment TN reduction than other solutions. An
additional axis isolates solutions that appear in Category 1 for all LGAs, as there were
numerous Category 1 solutions available in the LGA trade-off spaces. The indicator
shows none of the selected solutions lie in Category 1 for all LGAs. Determination of
how each solution performs with respect to all stakeholder objectives would be required
in order to better understand the compromises and return on investment for the CMA.
127 |
ADE | Figure 4-5 Breakdown by recipient LGA of the catchment management authority capital
expenditure for joint Pareto solutions. Colour axis shows the selected solutions. A lower
maximum category number indicates a solution that is likely to be preferable or equitable
to all stakeholders (in this case, since all LGA solutions were Category 1, maximum
category reflects the CMA category). BATNAs are not shown.
4.4.3.3 Identifying compromise solutions
Figure 4-6 shows the selected solutions, visualised on a screenshot of interactive many-
objective, multi-stakeholder trade-off space plots (BATNAs are not shown). The analyst
evaluated the performance of the selected solutions with respect to each stakeholder’s
values, by visualizing the solutions’ performance in each stakeholder objective space and
comparing each solution to the stakeholder’s preferred options. The stakeholder evaluated
the relative performance of other stakeholder solutions with their own BATNA and own
selected solutions. An analyst recorded the likelihood that each stakeholder will accept
each solution, and the rationale for the evaluation, shown in Table 4-7. A “yes” was
recorded where there was a large increase in benefits at similar cost or lower costs with
similar benefit, compared to solutions suggested by the stakeholder; a “maybe” was
recorded if there was an increase in some benefits and not others at additional cost; a “no”
was recorded where costs were higher with small or no increases in benefits. Recording
the rationale may be useful for further bargaining.
In the “CMA low $” solution, all stakeholders are likely to be satisfied with the solution
except LGA 2, who is concerned about a lower benefit in both stormwater harvesting
capacity and green score compared to their BATNA. To assist with identifying a
compromise solution that agrees with LGA2’s values, stakeholders can consider the
128 |
ADE | Table 4-7 Indicative stakeholder preferences for selected solutions
CMA LGA 1 LGA LGA 2 LGA 3
CMA LGA 1 LGA 3
Stakeholder High High 2 Low High High
Low $ Low $ Low $
Ben. Ben. $ Ben. Ben.
CMA Yes Yes Yes No No Yes Yes
Maybe
Reason low TN low TN
LGA 1 Yes Yes Maybe Maybe Yes No
Yes Yes
Category Category high low Categor low
Reason
1 1 cost Green y 1 SWH
LGA 2 Maybe Maybe Yes Yes Yes Yes No No
low low low low
Reason
benefit benefit SWH SWH
LGA 3 Yes Maybe No No Yes Maybe Yes Yes
low low low low
Reason
SWH benefit SWH SWH
Viable? Maybe Maybe No No Maybe No No No
4.5 Summary and conclusions
In this study, a general optimization-visualisation framework that deals with multiple
stakeholders with multiple objectives, and encourages a negotiated outcome for a
portfolio optimization problem, was presented. The framework addresses the need for a
decision support approach for identifying solutions to complex environmental problems
that i) handles multiple stakeholder formulations of the problem reflecting their interests
and values, ii) enables interactive exploration and analysis of possible solutions by
stakeholders, iii) encourages stakeholder trust in the final selected solution, and iv)
facilitates a final negotiated outcome. Improvements on existing multi-stakeholder
exploration approaches were developed. These include visualisation of the full trade-offs
between extremely large numbers of objectives using multiple linked parallel coordinate
plots in a visual analytics package. Solutions were framed within the plots to compare
proposed solutions to a best alternative across multiple objectives. This was done to
facilitate negotiation by emphasising the benefits gained and losses prevented through
accepting a negotiated outcome. This also highlights inequities between stakeholders and
facilitates bargaining where equitable outcomes are available
131 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.