Q-Learning Driven Multi-objective Hybrid PSO for Distributed Heterogeneous Hybrid Flow-shop Scheduling Problem

With the rapid advancement of Industry 5.0, the impact of worker resource constraints on scheduling problems has become increasingly significant. The Distributed Heterogeneous Hybrid Flow-shop Scheduling Problem with Worker constraints (DHHFSP-W) has emerged as an important extension of traditional Flow-shop Scheduling Problem (FSP). To address this NP-hard problem, this paper aims to minimize Total Energy Consumption (TEC) and Worker Costs (WC) by proposing a Q-learning driven Multi-objective Hybrid Particle Swarm Optimization (QL-MOHPSO) algorithm based on four vectors encoding. The algorithm integrates a hybrid sampling strategy combining VEGA and PDDR-FF to divide particles into three subgroups and employs a Q-learning driven multi-group search strategy to effectively balance solution diversity and convergence. Furthermore, to enhance solution quality, eight local search strategies are designed for specific vectors. Experimental results demonstrate that QL-MOHPSO exhibits superior performance across small, medium, and larger-scale instances, significantly outperforming six benchmark algorithms. This study provides an efficient and reliable optimization approach for addressing complex scheduling problems.