Fast Pareto set approximation for multi-objective flexible job shop scheduling via parallel preference-conditioned graph reinforcement learning

The Multi-Objective Flexible Job Shop Scheduling Problem (MOFJSP) is a complex challenge in manufacturing, requiring balancing multiple, often conflicting objectives. Traditional methods, such as Multi-Objective Evolutionary Algorithms (MOEA), can be time-consuming and unsuitable for real-time applications. This paper introduces a novel Graph Reinforcement Learning (GRL) approach, named Preference-Conditioned GRL, which efficiently approximates the Pareto set for MOFJSP in a parallelized manner. By decomposing the MOFJSP into distinct sub-problems based on preferences and leveraging a parallel multi-objective training algorithm, our method efficiently produces high-quality Pareto sets, significantly outperforming MOEA methods in both solution quality and speed, especially for large-scale problems. Extensive experiments demonstrate the superiority of our approach, with remarkable results on large instances, showcasing its potential for real-time scheduling in dynamic manufacturing environments. Notably, for large instances (50 × 20), our approach outperforms MOEA baselines with remarkably shorter computation time (less than 1% of that of MOEA baselines). The robust generalization performance across various instances also highlights the practical value of our method for decision-makers seeking optimized production resource utilization.