A Q-Learning-Based Multi-Phase Grey Wolf Optimization Algorithm for Distributed No-Wait Job Shop Problem

As an extension of the no-wait job shop scheduling problem, the distributed no-wait job shop scheduling problem (DNWJSP) combining distributed scheduling with no-wait constraint exists commonly in real-world manufacturing. In this study, we formulate a mixed-integer linear programming (MILP) model for the problem and propose a Q-learning-based multi-phase grey wolf optimization (QMGWO) algorithm. First, the algorithm consists of two phases: the hunting phase and the local search phase. In the hunting phase, the information from three best solutions in the population is used to determine the search mode and reallocate some jobs for the current solution. In the local search phase, a local search is designed and performed on the solutions obtained from the hunting phase. Then, to prevent the algorithm from falling into local optimum, we design six local search strategies based on the key factory. Furthermore, to enhance the flexibility and efficiency of the algorithm, we propose a Q-learning method to dynamically select an appropriate local search strategy. Finally, the experimental results and statistical analysis based on benchmark instances demonstrate that the QMGWO algorithm has a significant advantage over several other high-performing algorithms. In addition, we validate the optimal solutions for all small instances by applying the CPLEX solver to the MILP model.