A Bi-Population Competition Adaptive Interior Search Algorithm Based on Reinforcement Learning for Flexible Job Shop Scheduling Problem

In this paper, a bi-population competition adaptive interior search algorithm (BCAISA) based on a reinforcement learning strategy is proposed for the classical flexible job shop scheduling problem (FJSP) to optimize the makespan. First, the scheduling solution is represented using a machine-job-based two-segment integer encoding method, and various heuristic rules are then applied to generate the initial population. Secondly, a bi-population mechanism is introduced to partition the population into two distinct sub-populations. These sub-populations are specifically tailored for machine assignment and operation permutation, employing different search strategies respectively, aiming to facilitate an efficient implementation of parallel search. A competition mechanism is introduced to facilitate the information exchange between the two sub-populations. Thirdly, the ISA is adapted for the discrete scheduling problem by discretizing a series of search operators, which include composition optimization, mirror search, and random walk. A Q-learning-based approach is proposed to dynamically adjust a key parameter, aiming to strike a balance between the capacity for global exploration and local exploitation. Finally, extensive experiments are conducted based on 10 well-known benchmark instances of the FJSP. The design of the experiment (DOE) method is employed to determine the algorithm’s parameters. Based on the computational results, the effectiveness of four improvement strategies is first validated. The BCAISA is then compared with fifteen published algorithms. The comparative data demonstrate that our algorithm outperforms other algorithms in 50% of benchmark instances. Additionally, according to the relative percentage deviation (RPD) from the state-of-the-art results, the BCAISA also exhibits superior performance. This highlights the effectiveness of our algorithm for solving the classical FJSP. To enhance the practical application, the scope of the ISA will be broadened in future work to more complex problems in real-world scenarios.