Enhanced salp swarm algorithm based on firefly algorithm for unrelated parallel machine scheduling with setup times

Unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times has received more attention due to its various industrial and scheduling applications. However, the UPMSP is considered an NP-hard problem, even without setup times. Moreover, the sequence-dependent setup times presents more complexity, which makes finding an optimal solution is very hard. In this paper, a modified salp swarm algorithm (SSA) based on the firefly algorithm (FA) is proposed to enhance the quality of the solution of UPMSP. The proposed approach, called SSAFA, uses the operators of FA to improve the exploitation ability of SSA by working as a local search. We evaluate the proposed SSAFA using both small and large problem instances. Furthermore, extensive comparisons to several existing metaheuristic methods used to solve UPMSP problems have been carried out. The evaluation outcomes confirmed the competitive performance of the proposed SSAFA in all problem instances, using different performance measures.