روش ε-محدودیت اصلاح شده برای مسائل بهینه سازی دوهدفه: کاهش پیچیدگی محاسباتی و افزایش کارایی

محورهای موضوعی : آمار

آرمین قانع کنفی ¹ (استادیار، گروه ریاضی، دانشکده علوم پایه، دانشگاه آزاد اسلامی، واحد لاهیجان، لاهیجان، ایران.)

تاریخ دریافت : 1396/09/11 تاریخ پذیرش : 1400/08/05 تاریخ انتشار : 1400/09/01

کلید واژه: non-dominated points, &epsilon, -constraint method, Multiobjective optimization,

چکیده مقاله :

یکی از روش های مؤثر در حل مسائل بهینه سازی چندهدفه، روش ε-محدودیت می باشد که بر خلاف روش مجموع وزن دار شده قادر به یافتن نقاط غیرمغلوب در قسمت های نامحدب از مرز غیرمغلوب است. از معایب عمده این روش یافتن نقاط غیرمغلوب تکراری به ازای انتخاب پارامترهای متفاوت و در نتیجه افزایش پیچیدگی محاسباتی الگوریتم و کاهش کارایی آن در حالت کلی است که به لحاظ زمان و هزینه پیاده سازی مقرون به صرفه نیست. در این مقاله اصلاحی بر روش ε-محدودیت انجام می گیرد که به واسطه هوشمندسازی الگوریتم، نواحی غیرضروری که منجر به تولید نقاط غیرمغلوب تکراری می شوند، از همان ابتدا حذف می گردند و در نتیجه لزوم تلاش های محاسباتی اضافی جهت یافتن نقاط غیرمغلوب تکراری منتفی می شود. مباحث و جزییات روش پیشنهادی به همراه الگوریتم آن، ارائه شده و در بخش مثال های عددی، کارایی روش پیشنهادی در مقایسه با روش ε-محدودیت، مورد بررسی قرار می گیرد.

چکیده انگلیسی:

One of the effective method for solving the multi-objective optimization problems is the ε-constraint method which, unlike the weighted sum method is able to find non-dominated points in non-convex parts of the non-dominated frontier. The main disadvantages of this method are finding similar non-dominated points for choosing different parameters and thus increasing the computational complexity of the algorithm and reducing its overall performance, which is not cost-effective in terms of time and cost. In this paper, a modified is made to ε-constraint method, which, due to the intelligence of the algorithm, the unnecessary areas that lead to the production of the same non-dominated points are eliminated from the beginning. Therefore, additional computational efforts are eliminated to produce the same non-dominated points. Discussions and details of the proposed method, with its algorithm, are presented and in the numerical examples section, the efficiency of the proposed method is compared with the ε-constraint method.

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