An Improved Multi-Swarm Migrating Birds Optimization Algorithm for Hybrid Flow Shop Scheduling

Abstract

An improved multi-swarm migrating birds optimization (IMMBO) algorithm is proposed for hybrid flow shop scheduling with sequence-dependent setup times (HFS-SDST), to minimize the total maximum completion time (i.e., makespan). Permutation-based encoding is adopted to substitute the individual. The modified Nawaz-Enscore-Ham (MNEH) algorithm is employed to generate initial population which are assigned to each sub-swarm according to the makespan. For each sub-swarm, the neighborhood individuals of the leader and followers are generated respectively by performing serial and parallel neighborhood strategies. If the follower is better than the leader according to their makespan, they are exchanged to ensure the information interaction of individuals within the sub-swarm. Moreover, the discrete whale optimization strategy is embedded in IMMBO to optimize the leaders of all sub-swarms to enhance the interaction among them. Furthermore, the local search is designed for the optimal individual to further improve the local search ability of the algorithm. Meanwhile, to avoid algorithm premature convergence, the control strategy for population diversification is designed to the leader of each sub-swarm. Finally, based on adjusting the algorithm parameters experimentally, simulation experiments are conducted on four variants of IMMBO to verify the function of each part by testing an adaptation dataset of Ta. Moreover, the IMMBO is compared with three existing algorithms by testing an adaptation dataset of Ta, and the experimental results demonstrate the effectiveness of the IMMBO algorithm to solve the hybrid flow shop scheduling problem