نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی و آمار، دانشکده علوم پایه، دانشگاه گنبد کاووس، گنبد کاووس، ایران.

چکیده

مسئله‌ی برنامه­ریزی درجه دوم یکی از مهم‌ترین مسائل کلاسیک بهینه­سازی است که به جستجوی بیشینه یا کمینه‌ی یک تابع درجه دوم تحت قیود خطی تساوی یا نامساوی می­پردازد. در این مقاله، برنامه­ریزی درجه دوم که تمام پارامترهای آن اعداد فازی نامنفی باشد را مورد بررسی قرار می‌دهیم و یک الگوریتم جدید را مبتنی بر اعمال و حساب فازی، ارائه می­کنیم که مدل فازی را به سه مدل قطعی کوچک‌تر و ساده­تر تجزیه می‌کند. جواب بهین مدل فازی با حل مدل­های قطعی توسط الگوریتم‌های متداول همچون SQP و ترکیب این جواب‌ها تعیین می­شود. در انتها، یک مثال جهت پیاده­سازی و نشان دادن کارایی الگوریتم پیشنهادی حل می‌شود. 

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Fuzzy Quadratic Programming with Non-negative Parameters: A Solving method based on Decomposition

نویسندگان [English]

  • Nemat Allah Taghi-Nezhad
  • Fatemeh babakordi

Department of Mathematics, Faculty of Basic Science, Gonbad Kavous University, Gonbad Kavous, Iran.

چکیده [English]

Quadratic programming problem is one of the important problem of classic optimization problems that the aim is to find the maximum or minimum amount of a quadratic function under linear constraints. In this paper, the quadratic programming problem where its parameters are all nonnegative fuzzy numbers is discussed and a new algorithm based on fuzzy operations and fuzzy arithmetic is presented where reduced the fuzzy model into three smaller and more simple crisp problem. Then, by solving these crisp models using conventional algorithms such as SQP and by combining these solutions, the optimal solution of the fuzzy problem is obtained. Finally, an example is solved to implement the proposed algorithm and show the applicability of it.

کلیدواژه‌ها [English]

  • Fuzzy quadratic programming
  • Fuzzy set theory
  • Fuzzy constraints
  • Fuzzy ranking method
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