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Solving exactly Combinatorial Optimization Problems (COPs) using aBranch-and-Bound (B&B) algorithm requires a huge amount of computationalresources. Therefore, we recently investigated designing B&B algorithms on topof graphics processing units (GPUs) using a parallel bounding model. Theproposed model assumes parallelizing the evaluation of the lower bounds onpools of sub-problems. The results demonstrated that the size of the evaluatedpool has a significant impact on the performance of B&B and that it dependsstrongly on the problem instance being solved. In this paper, we design anadaptative parallel B&B algorithm for solving permutation-based combinatorialoptimization problems such as FSP (Flow-shop Scheduling Problem) on GPUaccelerators. To do so, we propose a dynamic heuristic for parameterauto-tuning at runtime. Another challenge of this work is to exploit largerdegrees of parallelism by using the combined computational power of multipleGPU devices. The approach has been applied to the permutation flow-shopproblem. Extensive experiments have been carried out on well-known FSPbenchmarks using an Nvidia Tesla S1070 Computing System equipped with two TeslaT10 GPUs. Compared to a CPU-based execution, accelerations up to 105 areachieved for large problem instances.

An Adaptative Multi-GPU based Branch-and-Bound. A Case Study: the Flow-Shop Scheduling Problem