ENHANCINGA MODIFIEDMETA-HEURISTIC APPROACH FOR NON-LINEAR BI-LEVEL PROGRAMMING PROBLEM
EGHBAL HOSSEINI *
Candidate at Payamenur University of Tehran, Department of Mathematics, Tehran, Iran
ISA NAKHAIKAMALABADI *
Professor of Industrial Engineering at University of Kurdistan, Sanandaj, Iran
*Author to whom correspondence should be addressed.
The bi-level programming problems (BLPP) are attractive for many researchers because of their application in several areas such as economic, traffic, finance, management, and so on. This form of mathematical programming is an appropriate tool to model these real problems. It has been proven that the general BLPP is an NP-hard problem, so the BLPP is a practical and complicated problem therefore solving this problem would be significant. In this paper, we attempt for developing an effective approach based on meta-heuristic algorithm which is the fast approximate method 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 the proposed approach. Finally, the smoothed problem is solved using the presented approach. The presented approach achieves 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, Karush-Kuhn-Tucker conditions, Meta-Heuristic algorithm