Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 402437, 13 pages
Research Article

An Auxiliary Function Method for Global Minimization in Integer Programming

School of Computer Science and Technology and Department of Applied Mathematics, School of Science, Xidian University, Xi'an, Shaanxi 710071, China

Received 22 July 2011; Revised 10 October 2011; Accepted 10 October 2011

Academic Editor: Blas M. Vinagre

Copyright © 2011 Hongwei Lin 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.


An auxiliary function method is proposed for finding the global minimizer of integer programming problem. Firstly, we propose a method to transform the original problem into an integer programming with box constraint, which does not change the properties of the original problem. For the transformed problem, we propose an auxiliary function to escape from the current local minimizer and to get a better one. Then, based on the proposed auxiliary function, a new algorithm to find the global minimizer of integer programming is proposed. At last, numerical results are given to demonstrate the effectiveness and efficiency of the proposed method.