Q-learning-based multi-objective particle swarm optimization with local search within factories for energy-efficient distributed flow-shop scheduling problem

Given the increasing severity of ecological issues, sustainable development and green manufacturing have emerged as crucial areas of research and practice. The continuous growth of the globalizing economy has led to the prevalence of distributed manufacturing systems. Distributed flow-shop scheduling problem (DFSP) is a complex NP-hard problem that involves two highly coupled sub-problems: job allocating for factories and job sequencing within factories. This paper proposes an efficient Q-learning-based multi-objective particle swarm optimization (QL-MoPSO) to address the DFSP, with the objectives of minimizing makespan and total energy consumption. The particle swarm optimization (PSO) algorithm has been enhanced by dividing particles into three subgroups, enabling faster convergence to three distinct areas of the Pareto Front (PF). Q-learning guides variable neighborhood search (VNS) as a local search strategy, balancing exploration and exploitation capabilities. To make the algorithm more reasonable and efficient for solving DFSP, multi-objective particle swarm optimization (MoPSO) uses the exchange sequence to update the job sequence vector, crossover and mutation to update the factory assignment vector. Computational experiments demonstrate that the proposed algorithm accelerates convergence and ensures good distribution performance and diversity, outperforming traditional multi-objective evolutionary algorithms.