A hybrid genetic algorithm for parallel machine scheduling with setup times:A comparative study of metaheuristics on large problem instances

This paper addresses the unrelated parallel machine scheduling problem with sequence and machine dependent setup times and machine eligibility constraints. The objective is to minimize the maximum completion time (makespan). Instances of more than 500 jobs and 50 machines are not uncommon in industry. Such large instances become increasingly challenging to provide high-quality solutions within limited amount of computational time, but so far, have not been adequately addressed in recent literature. A hybrid genetic algorithm is developed, which is lean in the sense that is equipped with a minimal number of parameters and operators, and which is enhanced with an effective local search operator, specifically targeted to solve large instances. For evaluation purposes a new set of larger problems is generated, consisting of up to 800 jobs and 60 machines. An extensive comparative study shows that the proposed method performs significantly better compared to other state-of-the-art algorithms, especially for the new larger instances. Also, it is demonstrated that calibration is crucial and in practice it should be targeted at a narrower set of representative instances