A Q-learning guided dual population genetic algorithm for distributed permutation flow shop scheduling problem with machine having fuzzy processing efficiency

The emergence of Industry 5.0 has shifted the focus of research towards green manufacturing, flexible and digitalized production, particularly emphasizing human–machine collaboration and distributed manufacturing systems. Such a transition introduces increasingly complex and dynamic challenges for manufacturing enterprises, resulting in heightened uncertainties in production scheduling where traditional scheduling approaches often exhibit limited capability in handling multi-objective trade-offs. To overcome these limitations, a $Q$-learning guided dual-population genetic algorithm (QGGA) is proposed in the current study, featuring two key innovations: (1) a cooperation pool with dual-population knowledge sharing that stores non-dominated solutions from both populations while maintaining their evolutionary independence, (2) a state-dependent action adaptation mechanism that dynamically selects actions from nine heuristic rules using $Q$-learning. The cooperation pool enables synergistic optimization by storing non-dominated solutions from both populations to enable knowledge exchange while preserving their independent optimization processes. The $Q$-learning component continuously optimizes action selection based on solution diversity metric and convergence metric. Experimental results demonstrate that the proposed method achieves 19.1% improvement in Hypervolume (HV) and 65.5% reduction in inverted Generational Distance (IGD) compared to NSGA-II, outperforms PPO by 24.8% HV, and achieves an 90.4%better IGD than MOEA/D, achieving superior balance between solution robustness and computational efficiency. This advancement provides a new methodological framework for addressing Industry 5.0 scheduling challenges under uncertainty.