Heuristics for planning with action costs

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 h(alpha)(s) is defined mathematically and handles non-uniform action costs like the additive heuristic ha, and yet like FF's heuristic h(FF), it encodes the cost of a specific relaxed plan and is therefore compatible with FF's helpful action pruning and its effective enforced hill climbing search. The definition of the set-additive heuristic is obtained from the definition of the additive heuristic, but rather than propagating the value of the best supports for a precondition or goal, it propagates the supports themselves, which are then combined by set-union rather than by addition. We report then empirical results on a planner that we call FF(h(alpha)(s)) that is like FF except that the relaxed plan is extracted from the set-additive heuristic. The results show that FF(h(alpha)(s)) adds only a slight time overhead over FF but results in much better plans when action costs are not uniform.