Graph search with A* is frequently faster than tree search. But A* graph search operates correctly only when the evaluation function is order-preserving. In the non-order-preserving case, no paths can be discarded and the entire explicit graph must be stored in memory. Such situations arise in one-machine minimum penalty job sequencing problems when setup times are sequence dependent. GREC, the unlimited memory version of a memory-constrained search algorithm of the authors called MREC, has a clear advantage over A* in that it is able to find optimal solutions to such problems. At the same time, it is as efficient as A* in solving graph search problems with order-preserving evaluation functions. Experimental results indicate that in the non-order-preserving case, GREC is faster than both best-first and depth-first tree search, and can solve problem instances of larger size than best-first tree search.
Sen, A. K., & Bagchi, A. (1996). Graph search methods for non-order-preserving evaluation functions: Applications to job sequencing problems. Artificial Intelligence, 86(1), 43–73. https://doi.org/10.1016/0004-3702(95)00094-1