MRLM: A meta-reinforcement learning-based metaheuristic for hybrid flow-shop scheduling problem with learning and forgetting effects

In the real -world production environment, the employee skills affect production efficiency. Especially, the learning and forgetting effects largely influence the processing time. This paper investigates a hybrid flowshop scheduling problem with learning and forgetting effects (HFSP-LF). Two learning and forgetting effects models are constructed. The sequence -dependent setup time (SDST) is also considered. The objective is to minimize the makespan of all jobs. To solve such problem, a mixed integer linear programming (MILP) model is built to formulate HFSP-LF. Then, a meta -reinforcement learning -based metaheuristic (MRLM) is proposed. In MRLM, a constructive heuristic is employed to generate the initial solution. Several problem -specific search operators are developed to explore and exploit the solution space. The search framework of MRLM comprises a meta -training phase and a Q -learning -driven search phase. In the meta -training phase, the search operators are trained to obtain prior knowledge of their selection and an initial learning model is constructed. In the Q -learning -driven search phase, Q -learning is employed to implement automatic selection of search operators through continuously perfecting the learning model and absorbing the feedback information of searching. Finally, we conduct a comprehensive experiment. The experimental results demonstrate that the designs of MRLM are effective, and MRLM significantly outperforms several well -performing methods on solving HFSP-LF.