A heuristic search approach for solving a minimum path problem requiring arc cost determination

Two generalizations of A*, BA* and DA*, are presented and analyzed. Both consider the problem of finding a minimum cost path from the start node to a finite goal node set in a directed OR-graph, assuming that estimates of the optimal costs from each node to the goal node set are given (as described by the heuristic function), estimates of all arc costs are given, but the actual arc costs require determination. DA* tends to determine a solution (not necessarily optimal) more rapidly than BA*. Improved admissible heuristics and arc cost estimates tend to reduce node expansions and arc cost determination steps for BA*; however, these results do not necessarily hold for DA*. We also show that BA* tends to require more arc cost determination steps and fewer node expansions than does DA*.