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Computational Intelligence and Neuroscience
Volume 2017, Article ID 1853131, 14 pages
https://doi.org/10.1155/2017/1853131
Research Article

The Artificial Neural Networks Based on Scalarization Method for a Class of Bilevel Biobjective Programming Problem

1School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
2School of Management, Huaibei Normal University, Huaibei 235000, China
3School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Correspondence should be addressed to Tao Zhang; moc.621@189htam_tz

Received 6 January 2017; Revised 19 May 2017; Accepted 7 August 2017; Published 14 September 2017

Academic Editor: Leonardo Franco

Copyright © 2017 Tao Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A two-stage artificial neural network (ANN) based on scalarization method is proposed for bilevel biobjective programming problem (BLBOP). The induced set of the BLBOP is firstly expressed as the set of minimal solutions of a biobjective optimization problem by using scalar approach, and then the whole efficient set of the BLBOP is derived by the proposed two-stage ANN for exploring the induced set. In order to illustrate the proposed method, seven numerical examples are tested and compared with results in the classical literature. Finally, a practical problem is solved by the proposed algorithm.