Planning with h ⁺ in Theory and Practice

Abstract

Many heuristic estimators for classical planning are based on the so-called delete relaxation, which ignores negative effects of planning operators. Ideally, such heuristics would compute the actual goal distance in the delete relaxation, i.e, the cost of an optimal relaxed plan, denoted by h ⁺. However, current delete relaxation heuristics only provide (often inadmissible) estimates to h ⁺ because computing the correct value is an NP-hard problem.

In this work, we consider the approach of planning with the actual h ⁺ heuristic from a theoretical and computational perspective. In particular, we provide domain-dependent complexity results that classify some standard benchmark domains into ones where h ⁺ can be computed efficiently and ones where computing h ⁺ is NP-hard. Moreover, we study domain-dependent implementations of h ⁺ which show that the h ⁺ heuristic provides very informative heuristic estimates compared to other state-of-the-art heuristics.