An Approach to Efficient Planning with Numerical Fluents and Multi-Criteria Plan Quality

Dealing with numerical information is practically important in many real-world planning domains where the executability of an
action can depend on certain numerical conditions, and the action effects can consume or renew some critical continuous resources,
which in PDDL can be represented by numerical fluents. When a planning problem involves numerical fluents, the quality of the
solutions can be expressed by an objective function that can take different plan quality criteria into account.
We propose an incremental approach to automated planning with numerical fluents and multi-criteria objective functions for
PDDL numerical planning problems. The techniques in this paper significantly extend the framework of planning with action graphs
and local search implemented in the LPG planner. We define the numerical action graph (NA-graph) representation for numerical
plans and we propose some new local search techniques using this representation, including a heuristic search neighborhood
for NA-graphs, a heuristic evaluation function based on relaxed numerical plans, and an incremental method for plan quality
optimization based on particular search restarts.Moreover, we analyze our approach through an extensive experimental study aimed
at evaluating the importance of some specific techniques for the performance of the approach, and at analyzing its effectiveness in
terms of fast computation of a valid plan and quality of the best plan that can be generated within a given CPU-time limit. Overall,
the results show that our planner performs quite well compared to other state-of-the-art planners handling numerical fluents.