Abstract
Unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times is considered a hot topic among the researchers, as it presents more complexity to be able to find an optimal solution. Many efforts have been made to solve UPMSP problems and established their performances. Therefore, in this study, a new method is introduced to address UPMSP problems with sequence-dependent and machine-dependent setup time. Our proposed method utilizes two meta-heuristic techniques, the whale optimization algorithm (WOA) and the firefly algorithm (FA), by combining their features to perform this task. The hybrid model is called WOAFA. For more detail, the operators of the FA are employed to improve the exploitation ability of the WOA by serving as a local search. Moreover, the quality of the proposed WOAFA method is tested by comparing with well-known meta-heuristic algorithms over six machines and six jobs, namely (2, 4, 6, 8, 10, and 12 machines) and (20, 40, 60, 80, 100, and 120 jobs).