Comparison between SA-based and EA-based Metaheuristics for Solving a Biobjective Unrelated Parallel Machine Scheduling Problem with Sequence Dependent Setup Times

The parallel machine scheduling problem with sequence dependent setup times is among the moststudied and hard combinatorial optimization problems, and has been investigated in depth by numerous researchers of both theoretical and practical interests. An extension of this problem to the case of unrelated parallel machines with multi-objective is evidently more complex, and its application can be found in industries such as TFT-LCD and automobile manufactures. The optimization criteria of the problem under study are to minimize total flow time and total tardiness. In this study, several notable multi-objective optimization metaheuristics are employed to solve the proposed scheduling problem: (1) two Pareto converging evolutionary algorithms (PCGAs), one of which uses random key as encoding scheme while the other of which uses job list, and (2) two multi-objective simulated annealing (MOSA) algorithms – SMOSA and UMOSA in the literature. The performances of these algorithms are compared using various convergence and diversity metrics as the evaluation standards, via two test instances generated according to a method introduced in the literature. The experimental results have shown that the PCGA with random key representation outperforms the other three in various convergence measures, and has found most of the reference solutions. Additionally, although the aforementioned PCGA does not provide the best distribution in terms of diversity, it excels in a measure applicable to evaluate the convergence as well as diversity.