Novel Hybrid Algorithm for Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup Time

This paper focuses on the hybrid flow shop scheduling problem with sequence-dependent setup time (HFSP-SDST) with minimizing the makespan. To address this problem, this paper designs a hybrid migrating birds optimization (HMBO) algorithm that integrates migrating birds optimization (MBO) algorithm, variable neighborhood descent search (VND) algorithm, problem-based local search (LS) algorithm, and constraint programming (CP) model. Specifically, HMBO consists of three primary stages. The first stage employs a hybrid algorithm (MBOVND) that integrates MBO and VND with permutation encoding and decoding. Because the solution space of permutation encoding and decoding cannot cover the full solutions of HFSP-SDST, LS and CP are used to enlarge the solution space of MBOVND in the second and third stages respectively. Specifically, LS algorithm is used in the second stage to explore the solutions that are not in the solution space of MBOVND, and CP model is used in the third phase to further enlarge the solution space of MBOVND and LS algorithm. The efficacy of the proposed VND, LS, CP, and HMBO are verified. Experimental results demonstrate that VND, LS, and CP are effective to improve the solving ability of MBO, and HMBO improves 89 out of the 120 best-known solutions for the benchmark instances.