A reinforcement learning based memetic algorithm for energy-efficient distributed two-stage flexible job shop scheduling problem

Given the increasingly severe environmental challenges, distributed green manufacturing has garnered significant academic and industrial interest. This paper addresses the distributed two-stage flexible job shop scheduling problem (DTFJSP) under time-of-use (TOU) electricity pricing, with the objective of minimizing both makespan and total energy consumption costs (TEC). To tackle the problem, a hybrid memetic algorithm (HMA) is proposed. Initially, a three-tier vector encoding scheme and three population initialization strategies are devised. Subsequently, global search operators are tailored to the problem's characteristics, and seven local search algorithms based on Q-learning are introduced. Additionally, an energy-saving operator is incorporated. Finally, orthogonal experimental design is employed to set algorithm parameters and validate the efficacy of some components. The numerical experimental results demonstrate that the proposed local search operator and energy-saving strategy are effective. Furthermore, the HMA exhibits superior diversity, breadth, and distribution compared to VNS, CMA, and NSGA-II, thereby validating the efficacy of the specialized designs of the HMA in addressing the DTFJSP.