A Cooperative Scatter Search With Reinforcement Learning Mechanism for the Distributed Permutation Flowshop Scheduling Problem With Sequence-Dependent Setup Times
Fuqing Zhao, Gang Zhou, Ling Wang
Abstract
The integration of reinforcement learning technology into meta-heuristic algorithms to address complex combinatorial optimization problems has attracted much attention in recent years. A cooperative scatter search with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning mechanism (QCSS) is proposed for solving the DPFSP-SDST. In the diversification generation method, two effective heuristic algorithms are designed to construct an initial population with high quality and diversity. In the improved method, eight domain knowledge-guided perturbation operators are combined with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -learning to balance the exploration and exploitation capabilities of the QCSS algorithm. The reference set (RefSet) is divided into two subpopulations, and adaptive competition is adopted between the subpopulations to enhance search efficiency. In addition, a restart mechanism is proposed in the RefSet update phase to ensure the diversity of solutions. The performance of the QCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the QCSS algorithm.