Abstract: To optimize the systematical operations and improve the energy efficiency of the Flexible Job-shop Scheduling Problem(FJSP),aiming at the minimization of comprehensive energy consumption,three energy-saving measures including machine selection,speed adjustment and timely switching on/off were simultaneously considered to establish a mixed integer linear programming model,and a co-evolutionary algorithm based on Deep Q-Network(DQN)was proposed to solve it.This algorithm inherited the advantages of strong pertinence and fast convergence of local search algorithms.Meanwhile,it incorporated co-evolution,so that the three sub-codes of processing sequence,machine selection and speed selection might cooperate and co-evolve.A local search operator recommendation mechanism based on DQN reinforcement learning was proposed,and hence the selected local search operators were more suitable for the current workshop operating status and were more conducive to reduction of energy consumption.A restart strategy based on archive set and cross operator was designed to push the algorithm to jump out of the local optimum.The experimental results showed that the proposed algorithm was significantly better than the comparison algorithms in terms of energy saving and stability.

Key words: flexible job-shop scheduling problem, energy-efficiency scheduling, co-evolutionary algorithm, operator recommendation, reinforcement learning

摘要： 为了优化柔性作业车间的系统运行,提升能效水平,以综合能耗最小为目标,以机器选择、速度调整和适时开关机3种节能策略同时实施为手段,建立混合整数线性规划模型,并提出基于深度Q网络的协同进化算法来求解。该算法继承了局部搜索算法问题针对性强、收敛速度快的优势,同时融入协同进化思想,使加工顺序、机器选择和速度等级选择三段子码合作竞争、共同进化;提出基于深度Q网络强化学习的局部搜索算子推荐机制,选配与当前车间运行状态更契合、更有利于节能降耗的局部搜索算子;设计了基于归档集、利用交叉操作的重启策略,推动算法跳出局部最优。实验结果表明,所提算法在能耗指标和稳定性方面显著优于对比算法。

关键词: 柔性作业车间, 能效调度, 协同进化算法, 算子推荐, 强化学习