【摘要】 针对分布式流水车间节能调度中最大完工时间（makespan）与总能耗（TEC）的多目标优化难题，本文提出一种基于强化学习的正弦优化算法（RLSOA）。算法通过双重Qlearning策略协同优化加工序列与速度调整：底层Q-learning优先加速关键路径任务以缩短makespan，顶层Q-learning降低非关键任务速度以减少TEC。结合自适应参数与4种速度调整算子，设计基于精英解导向的局部搜索策略，平衡全局探索与局部开发。基于480组不同规模算例的实验表明，相较于KCA、INSGA等对比算法，RLSOA在覆盖率（C-metric）和反世代距离（IGD）指标上平均提升23.6%和降低41.8%。消融实验验证双重Q-learning与局部搜索分别贡献65.3%和28.7%的解质量提升。统计检验（p<0.05）证实本文算法优越性，为分布式制造系统提供了高效的节能调度工具。更多还原

【Abstract】 To address the multi-objective optimization problem of minimizing makespan and total energy consumption(TEC) in energy-efficient distributed permutation flow shop scheduling(EEDPFSP), this paper proposes a reinforcement learning-based sine optimization algorithm(RLSOA). The algorithm integrates a dual Q-learning strategy: The bottom-level Q-learning prioritizes accelerating critical tasks to reduce makespan, while the top-level Qlearning adjusts processing speeds of non-critical tasks to lower TEC. An adaptive parameter derived from the sine formula dynamically controls the search scope, and a local search strategy guided by elite solutions balances global exploration and local exploitation. Experiments on 480 instances with varying scales demonstrate that RLSOA outperforms state-of-the-art algorithms(KCA and INSGA) with 23.6% higher C-metric and 41.8% lower IGD on average. Ablation studies reveal that the dual Q-learning and local search contribute 65.3% and 28.7% to solution quality improvement, respectively. Statistical tests(Friedman and Wilcoxon, p<0.05) confirm the superiority of RLSOA. The proposed algorithm provides an efficient tool for energy-efficient scheduling in distributed manufacturing systems.更多还原