Depth-first heuristic search for the job shop scheduling problem

We evaluate two variants of depth-first search algorithms and consider the classic job shop scheduling problem as a test bed. The first one is the well-known branch-and-bound algorithm proposed by P. Brucker et al. which uses a single chronological backtracking strategy. The second is a variant that uses partially informed depth-first search strategy instead. Both algorithms use the same heuristic estimation; in the first case, it is only used for pruning states that cannot improve the incumbent solution, whereas in the second it is also used to sort the successors of an expanded state. We also propose and analyze a new heuristic estimation which is more informed and more time consuming than that used by Brucker's algorithm. We conducted an experimental study over well-known instances showing that the proposed partially informed depth-first search algorithm outperforms the original Brucker's algorithm.