Hybrid artificial bee colony algorithm with Q-learning for distributed heterogeneous flexible job shop scheduling problem considering machine preventive maintenance

Current research on preventive maintenance in the scheduling domain predominantly focuses on machine degradation under stable operating conditions. However, the machine works under varying operating conditions (cutting depth, feed rate, etc.) when processing different jobs, and much research ignores the influence of these diverse operating conditions on machine degradation. To address this gap, this paper proposes a novel machine degradation model tailored to various operating conditions and introduces a dual-threshold preventive maintenance strategy, which is integrated with the scheduling problem. To effectively solve this integrated problem, a mixed-integer programming (MIP) framework targeting makespan minimization is constructed, coupled with a hybrid artificial bee colony (ABC) algorithm incorporating a neighborhood search mechanism. First, a three-layer encoding scheme based on factory-machine-operation is designed, and preventive maintenance decisions are incorporated into the decoding strategy. Furthermore, a hybrid population initialization strategy is developed to enhance population diversity. Third, multiple crossover and mutation operators are developed during the employed bee phase, and a simple yet effective operator selection mechanism is employed to improve global search efficiency. In the onlooker bee phase, five neighborhood search operators are proposed to address the local search limitations of traditional ABC algorithms. These operators are adaptively selected via a Q-learning algorithm to strengthen local search performance. Finally, extended computational instances are designed, and comparative experiments validate the effectiveness of the proposed algorithm in solving scheduling problems across different job scales and factory scales.