Two Approaches for Solving Non-linear Bi-level Programming Problem
Issue: 2015 - Volume 3 [Issue 5]
Eghbal Hosseini *
Department of Mathematics, Payamenur University of Tehran, Tehran, Iran
Isa Nakhai Kamalabadi
Industrial Engineering at University of Kurdistan, Sanandaj, Iran
*Author to whom correspondence should be addressed.
In the recent years, the bi-level programming problem (BLPP) is interested by many researchers and it is known as an tool to solve the real problems in several areas such as economic, traffic, finance, management, and so on. Also, it has been proven that the general BLPP is an NP-hard problem. In this paper, we attempt to develop two effective approaches, one based on approximate approach and the other based on the hybrid algorithm by combining the penalty function and the line search algorithm for solving the non-linear BLPP. In these approaches, by using the Karush-Kuhn-Tucker conditions the BLPP is converted to a non-smooth single problem, and then it is smoothed by Fischer-Burmeister functions. Finally, the smoothed problem is solved using both of the proposed approaches. The presented approaches achieve an efficient and feasible solution in an appropriate time which has been evaluated by comparing to references and test problems.
Keywords: Non-linear bi-level programming problem, approximate method, karush-kuhn-tucker conditions, line search method