An Improved Firefly Algorithm for the Unrelated Parallel Machines Scheduling Problem With Sequence-Dependent Setup Times

Research in the area of unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times has received little attention from the research community. However, this problem is NP-hard even without considering the setup times, and when sequence-dependent setup times are included, finding optimal solutions becomes very difficult, especially for the problems with large dimension. In this paper, a firefly algorithm (FA) which is refined with a local search solution improvement mechanism is presented to solve this problem, with the objective of reaching a near-optimum solution. Since the classical FA was originally designed for continuous optimization problems, a new solution representation scheme is designed to make the FA suitable for a combinatorial optimization problem such as the UPMSP. Three different popular metaheuristic algorithms are developed in parallel to verify and measure the effectiveness of the proposed algorithm. More so, the success of the novel firefly scheduling method is measured by comparing the quality of its solutions against the best-known methods from the literature. An exhaustive computational and statistical analysis is carried out to show an excellent performance of the new method on a large set of problem instances. The numerical results show that the improved FA is competitive, fast, and efficient and provide good quality solutions for both small and large problem instances.