Optimal Solving of Permutation-based Optimization Problems on Heterogeneous CPU/GPU Clusters

Abstract

We revisit the parallelization of Branch-and-Bound (B&B) algorithms on massively parallel and heterogeneous architectures integrating multi-core processors and GPU accelerators. We provide a comprehensive description of the incremental development of a B&B-algorithm for the exact resolution of large permutation-based combinatorial optimization problems (COP). In order to highlight the challenges related to the different levels of the algorithm, we proceed incrementally by increasing the complexity of the targeted hardware step-by-step (as shown in Fig. 1) from sequential to multi-core, to GPUs and multi-GPU systems and finally to heterogeneous clusters combining multi-core CPUs and accelerator devices. On a cluster composed of 9 GPU- accelerated compute nodes (130,000 CUDA cores) the described methodology reduces the resolution time for a hard instance of the flow shop scheduling problem (FSP) from 600 hours (using 300 CPUs) to 9 hours1. Three permutation problems with different computational characteristics are used for experimental evaluation: FSP, quadratic assignment (QAP) and the N-Queens problem.