Abstract

In this paper, we consider the job shop scheduling problem (JSS) with non-anticipatory, per-machine, sequence-dependent setup times (SDST). The contributions of this paper are twofold. First, we propose a formulation in the form of a mixed-integer linear programming (MILP) model to modelize the aforementioned problem. Second, we play a pioneering effort for the effective adaptation of a novel metaheuristic known as electromagnetism-like algorithm (EMA) to solve the foregoing problem under the minimization of makespan. Afterwards, we evaluate the performance of the proposed MILP model, the EMA, and other effective metaheuristic algorithms from the literature on two different sets of benchmarks: small-sized and large-sized instances. The rationale behind applying the MILP model and the other algorithms at the small-sized instances is to compare the solutions obtained by the metaheuristic algorithms and the optimal solutions obtained by the MILP model (optimality gap analysis). Subsequently, to demonstrate the competitiveness of the EMA against some effective algorithms in the literature, we conduct an experimental design based on Taillard's benchmark, which is considered as large-sized instances. The purpose of conducting this very experiment is to show whether the acceptable performance of the EMA is transferrable to large-sized instances. The computational evaluations simply manifest the superiority of our proposed algorithm vs the other high-performing algorithms over both small and large instances.

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