IJE TRANSACTIONS C: Aspects Vol. 30, No. 12 (December 2017) 1863-1869    Article in Press

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J. Rezaeian Zeidi, M. Zarei and K. Shokoufi
( Received: October 28, 2016 – Accepted in Revised Form: September 08, 2017 )

Abstract    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/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 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.


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


چکیده    این تحقیق، مسئله ماشین­های موازی نامرتبط با زمان آماده­سازی وابسته به توالی، زمان دسترس کارها و محدودیت پردازش کارها را مورد مطالعه قرار داده است. هدف، کمینه­سازی مجموع وزنی هزینه­های زود کرد و دیر کرد کارها و همچنین کمینه­سازی مجموع زمان­های تکمیل کارها می­باشد. برای مسئله مورد نظر، یک مدل خطی عدد صحیح مختلط ارائه گردیده شده است. همچنین از آنجایی که مسئله در دسته مسائل NP-Hard قرار دارد، برای حل مسائل در اندازه واقعی، یک الگوریتم مبتنی بر پارتو با نام CENSGA ارائه شده است. الگوریتم ارائه شده در شش معیار عملکردی با الگوریتم NSGA-II مورد مقایسه و اعتبار سنجی قرار گرفته شده است. نتایج بدست ­آمده به صورت آماری توسط آزمایش میانگین Mann–Whitney و آزمایش t مورد ارزیابی قرار داده شده­ است. نتایج حاصل از آزمایش t نشان می­دهد که الگوریتم CENSGA در چهار معیار از شش معیار به طور قابل توجهی عملکرد بهتری نسبت به الگوریتم NSGA-II داشته است. همچنین، نتایج آماری حاصل از آزمایش میانگین Mann–Whitney نشان می­دهد که عملکرد الگوریتم CENSGA در دو معیار از شش معیار بهتر از عملکرد الگوریتم NSGA-II بوده­ است. از اینرو، نتایج آزمایشات تجربی نشان دهنده کارایی بالا الگوریتم معرفی شده برای مسائل محتلف می­باشد.


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