مسأله برنامه ریزی هندسی چند جمله ای چند متغیره با قیود معادلات رابط فازی با ترکیب ماکسیمم-حاصلضرب

نویسندگان
الیاس شیوانیان
زهرا رضایی
دانشگاه بین المللی امام خمینی
چکیده
این مقاله به بررسی دسته ای از مسائل برنامه‌ریزی هندسی چندجمله‌ای با تابع هدف کمینه سازی و مشروط بر اینکه دستگاه معادلات رابطه سازی آن ترکیب ماکسیمم-حاصلضرب باشد می پردازد ازآنجا که ناحیه شدنی غیر محدب است روش های برنامه ریزی ابتدایی کاربردی نیست. پس از معرفی و تعاریف اولیه، ویژگی‌های ناحیه شدنی و جوابهای بهینه بررسی می شود. جواب بهینه از یک جواب ماکسیمم شدنی و تعداد متناهی جوابهای مینیمال شدنی تشکیل می شود. تعدادی قاعده برای آسان تر پیدا کردن جواب بهینه و کاهیده شدن مسئله اصلی ارائه می گردد. یک الگوریتم برای به دست آوردن جواب و مقدار بهینه تابع هدف مسئله تغییر یافته با تابع هدف چند فازی (چندگانه) با استفاده از روش شاخه و کران و تکنیک معادلات رابطه سازی پیشنهاد می گردد. سرانجام برای توضیح مفهوم، یک مثال ارائه می شود.
کلیدواژه‌ها
مسأله برنامه‌ریزی هندسی چند‌جمله‌ای چند‌متغیره
معادلات رابط فازی
ترکیب ماکسیمم-حاصلضرب
روش شاخه و کران

عنوان مقاله English

Posynomial geometric programming problem subject to max–product fuzzy relation equations

نویسنده English

Elyas Shivanian
چکیده English

In this article, we study a class of posynomial geometric programming problem (PGPF), with the purpose of minimizing a posynomial subject to fuzzy relational equations with max–product composition. With the help of auxiliary variables, it is converted convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. Some preliminary definitions are introduced. Since the feasible solutions are not convex the basic programming techniques are not applicable. It is shown that an optimal solution consists of a maximum feasible solution and finite number of minimal feasible solutions by an equivalent programming problem. In fact, there are a lot minimal solutions and to obtain all them is tedious steps, boring and time consuming. Furthermore, we propose some rules for full simplifying the problem. Then by using a branch and bound approach and fuzzy relational equations (FRE) path, it is presented an algorithm to achieve an optimal solution to the PGPF. Finally, a numerical experiment is given to illustrate the steps of the algorithm.

کلیدواژه‌ها English

Fuzzy relation inequality
Separable programming
Least square technique
Minimal solution
Max-Product composition
Fuzzy optimization
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