Metaheuristic algorithms for the hybrid flowshop scheduling problem

Abstract

The hybrid flowshop scheduling problem (HFSP) has been widely studied in the literature, as it has many real-life applications in industry. Even though many solution approaches have been presented for the HFSP with makespan criterion, studies on HFSP with total flow time minimization have been rather limited. This study presents a mathematical model, four variants of iterated greedy algorithms and a variable block insertion heuristic for the HFSP with total flow time minimization. Based on the well-known NEH heuristic, an efficient constructive heuristic is also proposed, and compared with NEH. A detailed design of experiment is carried out to calibrate the parameters of the proposed algorithms. The HFSP benchmark suite is used for evaluating the performance of the proposed methods. As there are only 10 large instances in the current literature, further 30 large instances are proposed as new benchmarks. The developed model is solved for all instances on CPLEX under a time limit, and the performances of the proposed algorithms are assessed through comparisons with the results from CPLEX and the two best-performing algorithms in literature. Computational results show that the proposed algorithms are very effective in terms of solution time and quality. Additionally, the proposed algorithms are tested on large instances for the makespan criterion, which reveal that they also perform superbly for the makespan objective. Especially for instances with 30 jobs, the proposed algorithms are able to find the current incumbent makespan values reported in literature, and provide three new best solutions.