International Journal of Life Science and Engineering
Articles Information
International Journal of Life Science and Engineering, Vol.1, No.3, Jul. 2015, Pub. Date: Jun. 16, 2015
Bi-Section Algorithm for Solving Linear Bi-Level Programming Problem
 Eghbal Hosseini, Department of Mathematics, Payamenur University of Tehran, Tehran, Iran.
 Isa Nakhai Kamalabadi, Department of Industry, University of Kurdistan, Sanandaj, Iran.
The bi-level programming problem (BLPP) is significant because of its application in several areas such as transportation, finance, management, computer science and so on. This problem is an appropriate tool to model these real problems. It has been proven that the general BLPP is an NP-hard problem. Therefore, the BLPP is a practical and complicated problem so solving this problem would be significant. In this paper, we attempt for developing an algorithm based on bi-section algorithm to solve BLPP. Using the Karush-Kuhn-Tucker conditions the bi-level programming problem is converted to a non-smooth single level problem, and then it is smoothed by heuristic method for using proposed bi-section algorithm. The smoothed problem is solved using bi-section algorithm which is an exact method for solving the problem. The presented approach achieves an efficient and feasible solution in an appropriate time which has been evaluated by solving test problems.
Bi-Section Algorithm, Linear Bi-Level Programming Problem, Karush-Kuhn-Tucker Conditions
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