A Q-Learning Evolutionary Algorithm for Solving the Distributed Mixed No-Idle Permutation Flowshop Scheduling Problem

In this paper, a Distributed Mixed No-Idle Permutation Flowshop Scheduling Problem with Sequence-Dependent Setup Times (DMNIPFSP/SDST) is studied. Firstly, a multi-objective optimization model with completion time (makespan), Total Energy Consumption (TEC), and Total Tardiness (TT) as objectives is established. Based on problem characteristics and multi-objective characteristics, a Q-Learning Evolutionary Algorithm (QLEA) is proposed. Secondly, in order to improve the quality and diversity of the initial solution, two improved initialization strategies are proposed. Based on the characteristics of the problem solved (In the distributed system, symmetry design is adopted to ensure that the load of each workstation is relatively balanced in different time periods, avoid resource waste or bottleneck, and achieve the goal of no idle.), a novel population updating mechanism is designed to balance the ability of global exploration and local development of the algorithm. At the same time, a variable neighborhood local search based on Q-Learning is used to refine the non-dominated solution, thus guiding the population evolution. Finally, the simulation results show that this method has good performance in solving the multi-objective DMNIPFSP/SDST and can provide good economic benefits for enterprises.