Exactly solving permutation-based optimization problems on heterogeneous CPU / GPU clusters

Introduction. The exact resolution of large-scale instances of combinatorial optimization problems (COPs) requires a huge amount of computational resources. The first exact resolution of Ta056 [2], an instance permutation flow-shop scheduling problem (FSP) [3], illustrates the required computational effort. Using B&B@Grid, a B&B algorithm designed for computational grids, the optimal solution was found with proof of optimality within 25 days, exploiting on average 328 processors belonging to 9 distinct clusters of the nation-wide experimental testbed Grid’5000 3. In 2006, the most of the processors in Grid’5000 were either mono-core or dual-core CPUs. Today, according to the latest Top500 (June 2017) ranking of the world’s largest supercomputers 4, 93% of the Top500 systems use processors at least 8 cores and 27% use processors with 18 or more cores. On the road towards exascale computing, the ranking confirms the trend towards increasingly heterogeneous systems, as a total of 91 systems on the list use accelerator/co-processor devices, 80% of which are GPUs. In addition to their energy-efficiency, many-core devices have the potential to significantly boost the performance of traditional processors. This motivated us to revisit the design and implementation of B&B for hybrid multi-core and multi-GPU platforms, from single-node systems to large-scale heterogeneous high performance computing clusters. [1, 5, 6] Our study focuses on permutation-based COPs using the FSP, the Quadratic Assignment Problem (QAP) and the n-Queens puzzle problem as test-cases.