Temporal Planning with Preferences and Time-Dependent Continuous Costs

Temporal planning methods usually focus on the objective of minimizing makespan. Unfortunately, this misses a large class of planning problems where it is important to consider a wider variety of temporal and non-temporal preferences, making makespan lower-order concern. In this paper we consider modeling and reasoning with plan quality metrics that are not directly correlated with plan makespan, building on the planner POPF. We begin with the preferences defined in PDDL3, and present a mixed integer programming encoding to manage the the interaction between the hard temporal constraints for plan steps, and soft temporal constraints for preferences. To widen the support of metrics that can be expressed directly in PDDL, we then discuss an extension to soft-deadlines with continuous cost functions, avoiding the need to approximate these with several PDDL3 discrete-cost preferences. We demonstrate the success of our new planner on the benchmark temporal planning problems with preferences, showing that it is the state-of-the-art for such problems. We then analyze the benefits of reasoning with continuous (versus discretized) models of domains with continuous cost functions, showing the improvement in solution quality afforded through making the continuous cost function directly available to the planner.