DoubleLayered Hybrid Neural Network Approach for Solving Mixed Integer Quadratic Bilevel Problems
 Shamshul Bahar Yaakob,
 Junzo Watada
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Abstract
In this paper we build a doublelayered hybrid neural network method to solve mixed integer quadratic bilevel programming problems. Bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. In this paper, mixed integer quadratic bilevel programming problem is transformed into a doublelayered hybrid neural network. We propose an efficient method for solving bilevel programming problems which employs a doublelayered hybrid neural network. A twolayered neural network is formulate by comprising a Hopfield network, genetic algorithm, and a Boltzmann machine in order to effectively and efficiently select the limited number of units from those available. The Hopfield network and genetic algorithm are employed in the upper layer to select the limited number of units, and the Boltzmann machine is employed in the lower layer to decide the optimal solution/units from the limited number of units selected by the upper layer.The proposed method leads the mixed integer quadratic bilevel programming problem to a global optimal solution. To illustrate this approach, several numerical examples are solved and compared.
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 Title
 DoubleLayered Hybrid Neural Network Approach for Solving Mixed Integer Quadratic Bilevel Problems
 Book Title
 Integrated Uncertainty Management and Applications
 Book Part
 III
 Pages
 pp 221230
 Copyright
 2010
 DOI
 10.1007/9783642119606_21
 Print ISBN
 9783642119590
 Online ISBN
 9783642119606
 Series Title
 Advances in Intelligent and Soft Computing
 Series Volume
 68
 Series ISSN
 18675662
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 VanNam Huynh ^{(2)}
 Yoshiteru Nakamori ^{(2)}
 Jonathan Lawry ^{(3)}
 Masahiro Inuiguchi ^{(4)}
 Editor Affiliations

 2. School of Knowledge Science, Japan Advanced Institute of Science and Technology
 3. Department of Engineering Mathematics, University of Bristol
 4. Graduate School of Engineering Science, Osaka University
 Authors

 Shamshul Bahar Yaakob ^{(5)} ^{(6)}
 Junzo Watada ^{(5)}
 Author Affiliations

 5. Graduate School of IPS, Waseda University, 27 Hibikino, Wakamatsu,Kitakyushu, 8080135, Fukuoka, Japan
 6. School of Electrical Systems Engineering, Universiti Malaysia Perlis, 02600, Jejawi, Perlis, Malaysia
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