الگوریتمی جدید برای پیدا کردن نقاط بهینه پارتو در مسائل بهینه‌سازی چندهدفه

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری-دانشکده ریاضی و علوم کامیپوتر، دانشگاه صنعتی امیرکبیر، تهران، ایران

2 استاد تمام-دانشکده ریاضی و علوم کامیپوتر، دانشگاه صنعتی امیرکبیر، تهران، ایران

3 استاد یار، دانشکده علوم ریاضی، دانشگاه صنعتی شاهرود، شاهرود، ایران

چکیده

در این مقاله یک روش اسکالرسازی اصلاح‌شده برای بدست آوردن مجموعه نقاط پارتو در مسائل بهینه‌سازی چندهدفه مورد بررسی قرار می‌گیرد. روش پیشنهادی، تعمیمی از روش‌های تقاطع مرزی نرمال محدودشده و روش پاسکلوتی-سرافینی می‌باشد. در ابتدا، مساله بهینه‌سازی مربوط به روش اصلاح‌شده را بررسی می‌کنیم و سپس الگوریتمی برای بدست آوردن مجموعه نقاط بهینه پارتو ارایه می‌دهیم. در ادامه، روابط بین جواب‌های بهینه مساله اسکالرسازی و جواب‌های کارا (ضعیف، سره) مسائل بهینه‌سازی چندهدفه را بررسی می‌کنیم. در واقع شرایط لازم برای جواب‌های کارا (ضعیف، سره) مسائل بهینه‌سازی چندهدفه را بدست می‌آوریم. نتایج حاصل شده بدون شرط تحدب ناحیه شدنی مساله چندهدفه برقرار می‌باشند. در ادامه یک الگوریتم جدید برای تقریب زدن مرز پارتوی مسائل چندهدفه ارایه می دهیم. چندین مثال را به کمک الگوریتم ارایه شده حل و نتایج را با روشهای موجود مقایسه می کنیم. نتایج حاصله نشان از کارایی رویکرد پیشنهاد شده نسبت به روشهای معروف موجود دارد.

کلیدواژه‌ها


عنوان مقاله [English]

A new algorithm for finding Pareto optimal points of multiobjective optimization problems

نویسندگان [English]

  • Fereshteh Akbari 1
  • Esmaile Khorram 2
  • Mehrdad Ghaznavi 3
1 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.
2 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
3 Assistant Professor-Shahrood University of Technology
چکیده [English]

In this paper, a modified scalarization technique for finding Pareto optimal points of multiobjective optimization problems is provided. The proposed method is a combination of the normal constraint and elastic constraint method. First, we introduce the optimization problem of the modified method and then we present an algorithm for obtaining the set of Pareto points. Thereafter, the relationship between optimal solutions of this scalarization problem and (weakly, properly) efficient solutions of the multiobjective optimization problems are analyzed. Indeed, some necessary conditions for (weak, proper) efficiency are presented. All the provided results are established without any convexity assumption. Furthermore, we propose a new algorithm for approximating the Pareto front of multiobjective optimization problems. We solve some test problems by applying the suggested algorithm and compare the results with some existing methods, including the epsilon-constraint method, the Pascolleti-Serafini method and the NBI method. The obtained results highlight the efficiency of our approach in comparison with examined methods.

کلیدواژه‌ها [English]

  • Multiobjective optimization problem
  • Scalarization
  • Normalization
  • Pareto points
  • Properly efficient solutions
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