A Reinforcement Learning Based Sine Optimization Algorithm for Energy-efficient Distributed Flow Shop Scheduling Problem

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 Q-learning 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 (jobs: 20-80, machines: 4-16, factories: 2-5) 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.