关键词: 柔性作业车间调度问题（FJSP）, 图神经网络, 深度强化学习, 注意力机制

Abstract: Aiming at the flexible job shop scheduling problem with the goal of minimizing completion time and total energy consumption, an integrated algorithm framework based on graph neural networks and deep reinforcement learning is proposed. Firstly, the characteristics of the flexible job shop scheduling problem are analyzed, and a disjunctive graph is introduced to transform the problem into a sequential decision problem, which is then modeled as a Markov decision process. Secondly, a two-stage scheduling strategy is designed based on attention mechanism, which removes redundant scheduling states during the training process and significantly improves computational efficiency. Finally, a 2S-PPO algorithm based on proximal policy optimization is designed for training the two-stage scheduling strategy, aiming to achieve a joint scheduling strategy that can quickly respond to process selection and machine allocation. Experimental proof through standard FJSP examples and FJSP examples with energy consumption instances demonstrates that the proposed algorithm has better learning performance and generalization performance compared to traditional priority scheduling rules and other deep reinforcement learning algorithms.

Key words: flexible job-shop scheduling problem (FJSP), graph neural network, deep reinforcement learning, attention mechanism