Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 171697, 11 pages
http://dx.doi.org/10.1155/2011/171697
Research Article

Identifying a Global Optimizer with Filled Function for Nonlinear Integer Programming

Wei-Xiang Wang,1 You-Lin Shang,2 and Lian-Sheng Zhang3

1Department of Mathematics, Shanghai Second Polytechnic University, Shanghai 201209, China
2Department of Mathematics, Henan University of Science and Technology, Luoyang 471003, China
3Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 27 March 2011; Revised 10 July 2011; Accepted 15 July 2011

Academic Editor: Rigoberto Medina

Copyright © 2011 Wei-Xiang Wang 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

This paper presents a filled function method for finding a global optimizer of integer programming problem. The method contains two phases: the local minimization phase and the filling phase. The goal of the former phase is to identify a local minimizer of the objective function, while the filling phase aims to search for a better initial point for the first phase with the aid of the filled function. A two-parameter filled function is proposed, and its properties are investigated. A corresponding filled function algorithm is established. Numerical experiments on several test problems are performed, and preliminary computational results are reported.