A bi-level algorithmic framework for the multi-objective flexible job shop scheduling problem

For the flexible job shop scheduling problem (FJSP), this study develops a multi-objective optimization model that simultaneously minimizes makespan and total energy consumption. To address the limited generalizability of conventional metaheuristic algorithms in scheduling applications, a Bi-Level Dynamic Metaheuristic Algorithm Framework (BLDMA) is proposed. Within this framework, the outer-layer metaheuristic optimizes the operation sequence, whereas the inner-layer metaheuristic dynamically adjusts the weights assigned to different machine-assignment rules. Through the interaction between the two layers, the framework can adapt its search strategy to the characteristics of the problem and the evolving search process. Computational results show that, compared with the corresponding baseline metaheuristic algorithms, the BLDMA framework achieves better non-dominated solution sets on the tested instances. These findings demonstrate the effectiveness and adaptability of the proposed framework for energy-aware flexible job shop scheduling.