基于GPU加速的超大型计算机求解大置换流水车间调度问题
Solving large permutation flow-shop scheduling problems on GPU-accelerated supercomputers
摘要：
置换流水车间调度中的最小完工时间问题是一个著名的组合优化难题。在E.在1993年的Taillard，23个案件近30年来一直没有解决。在本文中，我们提出了我们的尝试，解决这些情况下的最优使用并行分支定界树搜索的GPU加速让Zay超级计算机。我们报告了11个以前未解决的问题实例的精确解，并改进了8个实例的上界。这些问题的解决方案既需要算法改进，也需要利用千万亿次高性能计算平台的计算能力。所面临的挑战在于，在由数百个大规模并行加速器设备和多核处理器组成的分布式系统上，高效地执行高度不规则的细粒度搜索树的并行深度优先遍历。我们提出并讨论了我们的基于置换的B&B的设计和实现，并通过实验评估其并行性能高达384 V100 GPU（200万CUDA核心）和3840 CPU核心。最大解决实例的最优性证明需要大约64 CPU年的计算-使用256个GPU和超过400万个并行搜索代理，搜索树的遍历在13小时内完成，探索339个$\times 10^{12}$节点。
英文摘要：
Makespan minimization in permutation flow-shop scheduling is a well-known hard combinatorial optimization problem. Among the 120 standard benchmark instances proposed by E. Taillard in 1993, 23 have remained unsolved for almost three decades. In this paper, we present our attempts to solve these instances to optimality using parallel Branch-and-Bound tree search on the GPU-accelerated Jean Zay supercomputer. We report the exact solution of 11 previously unsolved problem instances and improved upper bounds for 8 instances. The solution of these problems requires both algorithmic improvements and leveraging the computing power of peta-scale high-performance computing platforms. The challenge consists in efficiently performing parallel depth-first traversal of a highly irregular, fine-grained search tree on distributed systems composed of hundreds of massively parallel accelerator devices and multi-core processors. We present and discuss the design and implementation of our permutation-based B&B and experimentally evaluate its parallel performance on up to 384 V100 GPUs (2 million CUDA cores) and 3840 CPU cores. The optimality proof for the largest solved instance requires about 64 CPU-years of computation -- using 256 GPUs and over 4 million parallel search agents, the traversal of the search tree is completed in 13 hours, exploring 339$\times 10^{12}$ nodes.
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