Pareto-based Multi-criteria Evolutionary Algorithm for a Parallel Machines Scheduling Problem with Sequence-dependent Setup Times

This paper addresses an unrelated multi-machine scheduling problem with sequence-dependent setup time, release date and processing set restriction to minimize the sum of weighted earliness/tardinesspenalties and the sum of completion times, which is known to be NP-hard. A Mixed Integer Programming (MIP) model is proposed to formulate the considered multi-criteria problem. Also, to solve the model for real-sized applications, a Pareto-based algorithm, namely controlled elitism nondominated sorting genetic algorithm (CENSGA), is proposed. To validate its performance, the algorithm is examined under six performance metric measures, and compared with a Pareto-based algorithm, namely NSGA-II. The results are statistically evaluated by the Mann–Whitney test and t-test methods. From the obtained results based on the t-test, the proposed CENSGA significantly outperforms the NSGA-II in four out of six terms. Additionally, the statistical results from Mann– Whitney test show that the performance of the proposed CENSGA is better than the NSGA- II in two out of six terms. Finally, the experimental results indicate the effectiveness of the proposed algorithm for different problems.

کلیدواژه ها:

Multi-objective optimization ، Unrelated parallel machine ، Just-in-time scheduling ، Controlled elitism non-dominated sorting ، genetic algorithm ، Mixed-integer programming ، Sequence-dependent setup time