Efficient Temporal Piecewise-Linear Numeric Planning with Lazy
  Consistency Checking
  State-of-the-art temporal planners that support continuous numeric effects
typically interweave search with scheduling to ensure temporal consistency. If
such effects are linear, this process often makes use of Linear Programming
(LP) to model the relationship between temporal constraints and conditions on
numeric fluents that are subject to duration-dependent effects. While very
effective on benchmark domains, this approach does not scale well when solving
real-world problems that require long plans. We propose a set of techniques
that allow the planner to compute LP consistency checks lazily where possible,
significantly reducing the computation time required, thus allowing the planner
to solve larger problem instances within an acceptable time-frame. We also
propose an algorithm to perform duration-dependent goal checking more
selectively. Furthermore, we propose an LP formulation with a smaller footprint
that removes linearity restrictions on discrete effects applied within segments
of the plan where a numeric fluent is not duration dependent. The effectiveness
of these techniques is demonstrated on domains that use a mix of discrete and
continuous effects, which is typical of real-world planning problems. The
resultant planner is not only more efficient, but outperforms most
state-of-the-art temporal-numeric and hybrid planners, in terms of both
coverage and scalability.
