The obvious way to use several admissible heuristics in A* is to take their maximum. In this paper we aim to reduce the time spent on computing heuristics. We discuss Lazy A*, a variant of A* where heuristics are evaluated lazily: only when they are essential to a decision to be made in the A* search process. We present a new rational meta-reasoning based scheme, rational lazy A*, which decides whether to compute the more expensive heuristics at all, based on a myopic value of information estimate. Both methods are examined theoretically. Empirical evaluation on several domains supports the theoretical results, and shows that lazy A* and rational lazy A* are state-of-the-art heuristic combination methods.

A* is often described as being `optimal', in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. n is re-inserted into the OPEN list, but with the f-cost of the next best child. This paper introduces an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* generates only the children with the same f-cost as the parent. EPEA* is generalized to its iterative-deepening variant, EPE-IDA*. For some domains, these algorithms yield substantial performance improvements. State-of-the-art results were obtained for the pancake puzzle and for some multi-agent pathfinding instances. Drawbacks of EPEA* are also discussed.