Evaluating the Effectiveness of Integrated Benders Decomposition Algorithm and Epsilon Constraint Method for Multi-Objective Facility Location Problem under Demand Uncertainty

Document Type: Research Paper

Authors

1 Department of Mechanical and Manufacturing Engineering, Faculty of Engineering, University Putra Malaysia, Malaysia

2 Australian Energy Research Institute and the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2032, Australia

3 Department of Mathematics, Faculty of Science, 43400 UPM Serdang, Selangor Malaysia,

4 Department of Electrical and Computer Engineering, University of New Brunswick, P.O. Box 4400-UNB, Fredericton, NB, Canada E3B 5A3

Abstract

One of the most challenging issues in multi-objective problems is finding Pareto optimal points. This paper describes an algorithm based on Benders Decomposition Algorithm (BDA) which tries to find Pareto solutions. For this aim, a multi-objective facility location allocation model is proposed. In this case, an integrated BDA and epsilon constraint method are proposed and it is shown that how Pareto points in multi-objective facility location model can be found. Results are compared with the classic form of BDA and the weighted sum method for demand uncertainty and deterministic demands. To do this, Monte Carlo method with uniform function is used, then the stability of the proposed method towards demand uncertainty is shown. In order to evaluate the proposed algorithm, some performance metrics including the number of Pareto points, mean ideal points, and maximum spread are used, then the t-test analysis is done which points out that there is a significant difference between aforementioned algorithms.

Keywords

Main Subjects


Article Title [Persian]

ارزیابی اثربخشی الگوریتم یکپارچه تجزیه بندرز و روش اپسیلون-محدودیت برای مساله موقعیت یابی چند هدفه تحت شرایط عدم قطعیت تقاضا

Authors [Persian]

  • ایمان رحیمی 1
  • سای هنگ تانگ 1
  • عبدالله احمدی 2
  • سی تی ازفانزیام بینتی احمد 1
  • لای سون لی 3
  • عادل شرف 4
1 گروه مهندسی صنایع و مکانیک، دانشکده مهندسی، دانشگاه پوترا مالزی
2 مؤسسة تحقیقات انرژی استرالیایی و مدرسه مهندسی برق وتکنولوژی، دانشگاه نیو سوت والز، سیدنی، استرالیا
3 گروه ریاضی، دانشکده علوم ، دانشگاه پوترا مالزی
4 گروه مهندسی برق و کامپیوتر، دانشگاه نیوبرانزویک، فردریکتون، کانادا
Abstract [Persian]

یکی از بزرگ‌ترین چالش‌ها در مسائل با ساختار چند هدفه، پیداکردن نقاط بهینة پارتوست. در این مقاله الگوریتم دقیقی بر اساس الگوریتم تجزیهبندرز [1](BDA) ارائه شده است که سعی در پیداکردن جواب‌های پارتو دارد. در همین راستا، روش یکپارچة BDA و محدودیت اپسیلون ارائه و چگونگی پیداکردن جواب‌های بهینة پارتو با استفاده از مدل چند هدفه نشان داده می‌شود. نتایج با مدل استاندارد BDA و روش مجموع وزن‌دارشده تحت شرایط قطعیت و عدم‌قطعیت تقاضا مقایسه می‌شود. در این راستا، روش مونت کارلو با تابع یکنواخت استفاده شده است. سپس، پایداری مدل پیشنهادشده در شرایط عدم‌قطعیت نشان داده می‌شود. برای ارزیابی الگوریتم پیشنهادشده، برخی معیارهای عملکرد، از جمله تعداد نقاط پارتو، نقطة ایده‌آل میانگین، و حداکثر گسترش استفاده ش. تحلیل آزمون t انجام‌شده حاکی از این است که تفاوت قابل‌توجهی بین الگوریتم‌های مذکور وجود دارد.
 


[1]. Benders Decomposition Algorithm

Keywords [Persian]

  • الگوریتم یکپارچة تجزیه
  • بهینه‌سازی چند هدفه
  • عدم قطعیت تقاضا
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