Materials and Energy Research CenterInternational Journal of Engineering1025-2495301220171201Pareto-based Multi-criteria Evolutionary Algorithm for Parallel Machines Scheduling Problem with Sequence-dependent Setup Times1863186973076ENKeyvan Shokoufi, Mazandaran University of Science and TechnologyJavad rezaeianIndustrial Engineering, Mazandaran University of Science and Technology, BMohsen Zarei, Mazandaran University of Science and TechnologyJournal Article19700101This 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/tardiness penalties 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 non-dominated 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 Mannâ€“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 Mannâ€“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.http://www.ije.ir/article_73076_0206e099bd9ad1d54af1a53028ae7e18.pdf