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The hm admissible heuristics for (sequential and temporal) regressionplanning are defined by a parameterized relaxation of the optimal cost functionin the regression search space, where the parameter m offers a trade-offbetween the accuracy and computational cost of theheuristic. Existing methodsfor computing the hm heuristic require time exponential in m, limiting them tosmall values (m andlt= 2). The hm heuristic can also be viewed as the optimalcost function in a relaxation of the search space: this paper presents relaxedsearch, a method for computing this function partially by searching in therelaxed space. The relaxed search method, because it computes hm onlypartially, is computationally cheaper and therefore usable for higher values ofm. The (complete) hm heuristic is combined with partial hm heuristics, for m =3,..., computed by relaxed search, resulting in a more accurate heuristic.  This use of the relaxed search method to improve on the hm heuristic isevaluated by comparing two optimal temporal planners: TP4, which does not useit, and HSP*a, which uses it but is otherwise identical to TP4. The comparisonis made on the domains used in the 2004 International Planning Competition, inwhich both planners participated. Relaxed search is found to be cost effectivein some of these domains, but not all. Analysis reveals a characterization ofthe domains in which relaxed search can be expected to be cost effective, interms of two measures on the original and relaxed search spaces. In the domainswhere relaxed search is cost effective, expanding small states iscomputationally cheaper than expanding large states and small states tend tohave small successor states.

Improving Heuristics Through Relaxed Search - An Analysis of TP4 and HSP*a in the 2004 Planning Competition