یک روش تسریع یافته برای مساله برنامه ریزی هندسی با محدودیت های معادلات رابطه فازی دو قطبی با عملگر ماکزیمم-ضرب

نوع مقاله : مقاله پژوهشی

نویسندگان

1 فارغ التحصیل دکتری، دانشکده ریاضی و علوم کامپیوتر، دانشگاه دامغان، دامغان، ایران

2 دانشیار، دانشکده ریاضی و علوم کامپیوتر، دانشگاه دامغان، دامغان، ایران

چکیده

در این مقاله، مساله مینیمم سازی یک تابع هدف هندسی با توان تک جمله ای با محدودیت های معادلات رابطه فازی دو قطبی با عملگر ترکیبی ماکزیمم-ضرب مورد مطالعه قرار می گیرد. این مقاله قصد دارد که با ساده سازی مساله، کران پایین تابع هدف آنرا بهنگام کند و الگوریتمی برای یافتن کران بالای ابتدایی برای مقدار هدف بهینه مساله براساس کران پایین ابتدایی (یا بهنگام شده) آن طراحی کند. سپس، یک روش شاخه و کران اصلاح شده براساس این کران برای حل مساله فوق توسعه می دهیم. یک الگوریتم کارا برای حل مساله با توجه به الگوریتم فوق و روش شاخه و کران توسعه یافته طراحی خواهیم کرد. با توجه به کران بالا و پایین پیشنهاد شده، روش شاخه و کران توسعه یافته تعداد گره های خیلی کمتری را برای پیدا کردن جواب بهینه بررسی می کند. از اینرو، میزان محاسبات بطور قابل ملاحظه ای کاهش می یابد. در پایان، یک مثال عددی برای توضیح الگوریتم و کارایی آن ارایه می شود.

کلیدواژه‌ها


عنوان مقاله [English]

An accelerated method for geometric programming problem subject to constraints of bipolar fuzzy relation equations with the max-product operator

نویسندگان [English]

  • Samaneh Aliannezhadi 1
  • Ali Abbasi Molai 2
1 Ph.D graduate, School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
2 Associate Professor, Faculty of Mathematics and Computer Science, Damghan University, Damghan, Iran
چکیده [English]

In this paper, the minimization problem of a geometric objective function with a single-term exponent subject to bipolar fuzzy relation equations is studied with the max-product composition operator. This paper intends to update the lower bound of its objective function by simplifying the problem and design an algorithm to find the initial upper bound for the optimal objective value of the problem based on its initial (or updated) lower bound. We then develop a modified branch-and-bound method based on the bound to solve the above problem. We also design an efficient algorithm to solve the problem according to the above algorithm and the developed branch-and-bound method. According to the proposed upper and lower bound, the developed branch-and-bound method examines a much less number of nodes to find the optimal solution. Hence, the rate of computations is significantly reduced. Finally, a numerical example is provided to illustrate the algorithm and its performance.

کلیدواژه‌ها [English]

  • Bipolar fuzzy relation equations
  • Geometric programming
  • Max-product operator
  • Modified branch-and-bound method
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