Extending a MILP Compilation for Numeric Planning Problems to Include Control Parameters

Although PDDL is an expressive modelling language for planning problems, a significant limitation is imposed on the structure of actions: the parameters of actions are restricted to values from finite (in fact, explicitly enumerated) domains. In real-world, there are parameters whose values have infinite (or highly large-sized) domains, they are called control parameters. Thus, modelling and reasoning with these parameters is indeed a requirement. Recent work investigated planning with these parameters.

While for classical planning, heuristic search is the state-of-the-art approach, the introduction of control parameters might introduce a high number of branching points. In addition, the inclusion of control parameters in the heuristic evaluation is still an open issue popcorn. Alternatively to heuristic search, several compilations to Boolean Satisfiability (SAT), Constraint Programming (CP) and Mixed Integer Linear Programming (MILP) have been proposed. In this work, we are interested in MILP compilations, as control parameters can be easily modelled as additional variables of the model, whose values are only constrained by the actions preconditions, but not by the actions effects. We present here an extension of the MILP compilation of numeric planning problem with instantaneous actions to include control parameters.