Efficient Multi-Start Gray Wolf Optimization Algorithm for the Distributed Permutation Flowshop Scheduling Problem with Preventive Maintenance

The distributed permutation flowshop scheduling problem (DPFSP) has received increasing attention in recent years, which always assumes that the machine can process without restrictions. However, in practical production, machine preventive maintenance is required to prevent machine breakdowns. Therefore, this paper studies the DPFSP with preventive maintenance (PM/DPFSP) aiming at minimizing the total flowtime. For solving the problem, a discrete gray wolf optimization algorithm with restart mechanism (DGWO_RM) is proposed. In the initialization phase, a heuristic algorithm that takes into consideration preventive maintenance and idle time is employed to elevate the quality of the initial solution. Next, four local search strategies are proposed for further enhancing the exploitation capability. Furthermore, a restart mechanism is integrated into algorithm to avert the risk of converging prematurely to a suboptimal solution, thereby ensuring a broader exploration of potential solutions. Finally, comprehensive experiments studies are carried out to illustrate the effectiveness of the proposed strategy and to verify the performance of DGWO_RM. The obtained results show that the proposed DGWO_RM significantly outperforms the four state-of-the-art algorithms in solving PM/DPFSP.