# محاسبه مرز کارای مدل دوسطحی خطی چندهدفه

نوع مقاله: مقاله پژوهشی

نویسندگان

گروه ریاضی، دانشگاه شهید چمران اهواز

چکیده

برنامه ریزی دو سطحی، مدلی برای مسایل بهینه سازی سلسله مراتبی است که دو تصمیم گیرنده با توابع هدف، متغیر ها و قید های متفاوتی وجود دارد. آلوز و همکارانش در ، روشی برای محاسبه مرز کارای مساله دو‌سطحی خطی با دو تابع هدف در سطح بالا و یک تابع هدف در سطح پایین ارائه دادند. در این مقاله ما روش آنها را برای حالتی که بیش از دو تابع هدف در هر دو سطح وجود دارد، تعمیم داده و با بهره‌گیری از تغییر متغیر مناسب، روش جدیدی برای محاسبه مرز کارای مساله دو‌سطحی خطی با توابع هدف کسری در سطح بالا ارائه می‌دهیم. نهایتاً کارآیی روش های پیشنهادی را با حل چند مثال عددی و مقایسه نتایج آنها با دیگر روش ها نشان می دهیم.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

### Computing the pareto frontier of a linear Multiobjective bi-level model

نویسندگان [English]

• Abbas Mehrabani
چکیده [English]

Bilevel programming is the model for hierarchical optimization problems in which there are two decision makers that have different objective functions, variables and constraints. Alves et al in, proposed a method for computing the Pareto frontier of bilevel linear problem with biobjective at the upper level and a single objective function at the lower level. In this paper, we extend their method for the situation in which there exists more than two objective function at both levels, and then by using a suitable exchange variable, we proposed a new method for computing the Pareto frontier of bilevel linear problem with fractional multi-objective at the upper level. Finally we will show the efficiency of the propsed approaches by solving a few numerical examples and comparing the results with other methods.

کلیدواژه‌ها [English]

• Bilevel programming
• Multi objective programming
• Pareto frontier
• mixed- integer programming
• Fractional programming

### مراجع

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### سابقه مقاله

• تاریخ دریافت: 27 خرداد 1394
• تاریخ بازنگری: 01 فروردین 1395
• تاریخ پذیرش: 28 اردیبهشت 1395