Solving large permutation flow-shop scheduling problems on GPU-accelerated supercomputers

TL;DR

This paper demonstrates how GPU-accelerated supercomputers can be used to solve large permutation flow-shop scheduling problems optimally, solving 11 previously unsolved instances and improving bounds on others through parallel branch-and-bound algorithms.

Contribution

It introduces a novel parallel branch-and-bound method optimized for GPU clusters, enabling the solution of large, complex scheduling problems previously considered intractable.

Findings

Solved 11 previously unsolved instances to optimality.

Achieved a 339 trillion node search in 13 hours using 256 GPUs.

Improved upper bounds for 8 problem instances.

Abstract

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.