A Q-learning-based improved multi-objective genetic algorithm for solving distributed heterogeneous assembly flexible job shop scheduling problems with transfers

With the advancement of economic globalization, the distributed heterogeneous factory environment has become the mainstream in manufacturing enterprises. Scheduling flexible job shops in such a production environment holds practical value. However, due to the high complexity of certain jobs, the transfer of jobs between different factories are often required in practical production to balance machine load rates. Accordingly, this study addresses the distributed heterogeneous assembly flexible job shop scheduling problem with transfers, aiming to minimize both the makespan and total energy consumption. First, a multi-objective optimization model is formulated to define the problem, wherein knowledge of factory assignment and processing sequence for operations is summarized. Subsequently, given the complexity of this problem, a Q-learning-based improved multi-objective genetic algorithm (QL-IMOGA) is proposed as an effective approach. Within the proposed algorithm, a hybrid population initialization method is designed, considering factory load balancing and the earliest product completion time, to generate a high-quality initial population. Furthermore, two types of crossover operators, four types of mutation operators, and six objective-oriented neighborhood search operators are devised to enhance the algorithm's exploration and exploitation capabilities. Q-learning is employed for adaptive adjustment of key parameters to improve both convergence speed and solution quality. The effectiveness of the proposed population initialization method and neighborhood search operators is validated through 15 test cases. The results demonstrate that the proposed algorithm significantly outperformed four advanced meta-heuristic algorithms. Furthermore, it is observed that the solution employing the job transfer strategy led to an average reduction of 7.5% in makespan, a 3.9% decrease in total energy consumption, and an 8.4 % improvement in factory load rates compared to the solution using the job no-transfer strategy.