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.

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.

The hybrid flow shop group scheduling problem (HFGSP) with the delivery time windows has been widely studied owing to its better flexibility and suitability for the current just-in-time production mode. However, there are several unresolved challenges in problem modeling and algorithmic design tailored for HFGSP. In our study, we place emphasis on the constraint of timeliness. Therefore, this paper first constructs a mixed integer linear programming model of HFGSP with sequence-dependent setup time and delivery time windows to minimize the total weighted earliness and tardiness (TWET). Then a penalty groups-assisted iterated greedy integrating idle time insertion ( $\mathrm{P}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{T}\mathrm{I}$) is proposed to solve the above problem. In the $\mathrm{P}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{T}\mathrm{I}$, a double decoding strategy is proposed based on the earliest available machine rule and the idle time insertion rule to calculate the TWET value. Subsequently, to reduce the amount of computation, a skip-based destruction and reconstruction strategy is designed, and a penalty groups-assisted local search is proposed to further improve the quality of the solution by disturbing the penalized groups, i.e., early and tardy groups. Finally, through comprehensive statistical experiments on 270 test instances, the results prove that the proposed algorithm is effective compared to four state-of-the-art algorithms.