Set-Additive and TSP Heuristics for Planning with Action Costs and Soft Goals

We introduce a non-admissible heuristic for planning with action costs, called the set-additive heuristic, that combines the benefits of the additive heuristic used in the HSP planner and the relaxed plan heuristic used in FF. The set-additive heuristic is defined mathematically and handles non-uniform action costs like the additive heuristic but like FF’s heuristic, it encodes the cost of a specific relaxed plan and hence is compatible with FF’s helpful action pruning and its enforced hill climbing search. The set-additive heuristic changes the definition of the additive heuristic slightly by associating with each atom a relaxed plan rather than its numeric cost. The new formulation is used then to introduce a further variation that takes certain delete information into account by forcing the values of certain multivalued variables in the relaxed plan to be spanned by a path rather than by a tree. Finally, we show how soft goals can be compiled away and report empirical results using a modification of the FF planner that incorporates these ideas, leading to a planner that is as robust as FF but capable of producing better plans in a broader set of contexts.