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This work presents a new parallel procedure designed to process combinatorial branch-and-bound (B&B) algorithms by using GPU. Our strategy is to perform B&B sequentially until a specific depth, saving the current path in the B&B tree as a node into the Active Set, and then force the backtracking. Each node into the Active Set is a DFS-B&B root that will be concurrently processed by the GPU. We compare our results with multicore and serial versions of the same search schema, using explicit enumeration (all possible solutions) and implicit enumeration (branch-and-bound search), for some asymmetrical traveling salesman problem instances. Our computational results indicate the superiority of our GPU computing-based method mainly for the B&B's worst case.

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