Volume 10, Issue 1 (4-2015)
IJMSI 2015, 10(1): 1-10 |
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Saraj M, Safaei N. Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems. IJMSI 2015; 10 (1) :1-10
URL: http://ijmsi.ir/article-1-281-en.html
URL: http://ijmsi.ir/article-1-281-en.html
Abstract:
In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution.
Keywords: Bi-level programming, Fractional programming, Taylor Series, Kuhn-Tucker conditions, Goal programming, Penalty function.
Type of Study: Research paper |
Subject:
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