A Knowledge-Guided Deep Reinforcement Learning Approach for Energy-Aware Distributed Flexible Job Shop Scheduling with Job Priority

Energy-aware distributed manufacturing has become a key focus in modern production systems due to the growing demand for sustainable and efficient operations. This study investigates the energy-aware distributed flexible job shop scheduling problem with job priority, where multiple factories cooperate to process prioritized jobs under energy consumption considerations. Considering job priorities is essential for reflecting the practical importance and urgency of different customer orders, which directly affects scheduling fairness and production responsiveness. The proposed bi-objective model aims to simultaneously minimize total weighted tardiness and total energy consumption, accounting for both processing and idle power. To effectively solve this complex NP-hard problem, a knowledge-guided deep reinforcement learning approach is developed. Domain knowledge is integrated into a double deep Q-network to guide the adaptive selection of local search operators, while a co-evolutionary mechanism maintains global exploration and accelerates convergence. Extensive computational experiments are conducted on 24 benchmark instances, which are categorized into five groups according to factory scale, with the maximum problem size reaching 160 jobs × 6 machines × 5 factories, together with a real-world case study. Compared with four state-of-the-art multi-objective baseline algorithms (NSGA-II, MOPSO, MOEA/D, and SPEA2), the proposed D2QN-COEA demonstrates substantial performance advantages. On average, it achieves an HV improvement of 23.1% compared with the best-performing baseline on each instance, while GD and IGD are reduced by 70.8% and 63.7%, respectively. When averaged across all four baseline algorithms, D2QN-COEA yields improvements of 203.4% in HV, 83.9% in GD, 79.9% in IGD, and 70.8% in Spacing, confirming its superior convergence accuracy and solution diversity. The results confirm that embedding domain knowledge into deep reinforcement learning enhances optimization robustness and provides an intelligent solution for energy-efficient distributed scheduling in modern manufacturing systems.