Solving Non-Linear Bi-Level Programming Problem Using Taylor Algorithm

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Author(s): Eghbal Hosseini (Payamenur University of Tehran, Iran), Isa Nakhai Kamalabadi (University of Kurdistan, Iran)and Fatemah Daneshfar (University of Kurdistan, Iran)
Copyright: 2016
Pages: 14
Source title: Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics
Source Author(s)/Editor(s): Pandian Vasant (University of Technology Petronas, Malaysia), Gerhard-Wilhelm Weber (Middle East Technical University, Turkey)and Vo Ngoc Dieu (Ho Chi Minh City University of Technology, Vietnam)
DOI: 10.4018/978-1-4666-9644-0.ch030

Keywords: Algorithms / Artificial Intelligence / Computer Science & IT / Information Science Reference

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Abstract

In recent years the bi-level programming problem (BLPP) is interested by many researchers and it is known as an appropriate tool to solve the real problems in several areas such as economic, traffic, finance, management and so on. Also it has been proved that the general BLPP is an NP-hard problem. The literature shows a few attempts for using approximate methods. In this chapter we attempt to develop an effective approach based on Taylor theorem to obtain an approximate solution for the non-linear BLPP. In this approach using the Karush-Kuhn–Tucker, the BLPP has been converted to a non-smooth single problem, and then it is smoothed by the Fischer – Burmeister function. Finally the smoothed problem is solved using an approach based on Taylor theorem. The presented approach achieves an efficient and feasible solution in an appropriate time which is evaluated by comparing to references and test problems.

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