A Knowledge Representation Approach to Automated Mathematical Modelling
  In this paper, we propose a new mixed-integer linear programming (MILP) model
ontology and a novel constraint typology of MILP formulations. MILP is a
commonly used mathematical programming technique for modelling and solving
real-life scheduling, routing, planning, resource allocation, and timetabling
optimization problems providing optimized business solutions for industry
sectors such as manufacturing, agriculture, defence, healthcare, medicine,
energy, finance, and transportation. Despite the numerous real-life
Combinatorial Optimization Problems found and solved and millions yet to be
discovered and formulated, the number of types of constraints (the building
blocks of a MILP) is relatively small. In the search for a suitable
machine-readable knowledge representation structure for MILPs, we propose an
optimization modelling tree built based upon an MILP model ontology that can be
used as a guide for automated systems to elicit an MILP model from end-users on
their combinatorial business optimization problems. Our ultimate aim is to
develop a machine-readable knowledge representation for MILP that allows us to
map an end-user's natural language description of the business optimization
problem to an MILP formal specification as a first step towards automated
mathematical modelling.
