Significant advances have occurred in heuristic search for planning in the last eleven years. Many of these planners use A{sup}*-style search. We report on five sound and complete domain-independent forward state-space STRIPS planners in this paper. The planners are AWA{sup}* (Adjusted Weighted A{sup}*), MAWA{sup}* (Modified AWA{sup}*), AWA{sup}*-AC (AWA{sup}* with action conflict-based adjustment), AWA{sup}*-PD (AWA{sup}* with deleted preconditions-based adjustment), and AWA{sup}*-AC-LE (AWA{sup}*-AC with lazy evaluation). AWA{sup}* is the first planner to use node-dependent weighting in A{sup}*. MAWA{sup}*, AWA{sup}*-AC, AWA{sup}*-PD, and AWA{sup}*-AC-LE use conditional two-phase heuristic evaluation. MAWA{sup}* applies node-dependent weighting to a subset of the nodes in the fringe, after the two-phase evaluation. One novel idea in AWA{sup}*-AC-LE is lazy heuristic evaluation which does not construct relaxed plans to compute heuristic values for all nodes. We report on an empirical comparison of AWA{sup}*, MAWA{sup}*, AWA{sup}*-AC, AWA{sup}*-PD, and AWA{sup}*-AC-LE with classical planners AltAlt, FF, HSP-2 and STAN 4. Our variants of A{sup}* outperform these planners on several problems. The empirical evaluation shows that heuristic search planning is significantly benefitted by node-dependent weighting, conditional two-phase heuristic evaluation and lazy evaluation. We report on the insights about inferior performance of our planners in some domains using the notion of waiting time. We discuss many other variants of A{sup}*, state-space planners and directions for future work.
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