The cost of an optimal delete relaxed plan, known as h~+, is a powerful admissible heuristic but is in general intractable to compute. In this paper we examine the problem of computing h~+ by encoding it as a Maxsat problem. We develop a new encoding that utilizes constraint generation to supports the computation of a sequence of increasing lower bounds on h~+. We show a close connection between the computations performed by a recent approach to solving Maxsat and a hitting set approach recently proposed for computing h~+. Using this connection we observe that our MAXSAT computation can be initialized with a set of landmarks computed via cheaper methods like LM-cut. By judicious use of Maxsat solving along with a technique of lazy heuristic evaluation we obtain speedups for finding optimal plans over LM-cut on a number of domains. Our approach enables the exploitation of continued progress in Maxsat solving, and also makes it possible to consider computing or approximating heuristics that are even more informed that h~+ by, for example, adding some information about deletes back into the encoding.
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