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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 931092, 13 pages
Research Article

Solving Packing Problems by a Distributed Global Optimization Algorithm

1Department of Information Management, National Formosa University, Yunlin 632, Taiwan
2Institute of Information Management, National Chiao Tung University, No. 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
3Department of Business Management, National Taipei University of Technology, No. 1, Sec. 3, Chung Hsiao E. Road, Taipei 10608, Taiwan

Received 23 February 2012; Accepted 9 May 2012

Academic Editor: Yi-Chung Hu

Copyright © 2012 Nian-Ze Hu 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.


Packing optimization problems aim to seek the best way of placing a given set of rectangular boxes within a minimum volume rectangular box. Current packing optimization methods either find it difficult to obtain an optimal solution or require too many extra 0-1 variables in the solution process. This study develops a novel method to convert the nonlinear objective function in a packing program into an increasing function with single variable and two fixed parameters. The original packing program then becomes a linear program promising to obtain a global optimum. Such a linear program is decomposed into several subproblems by specifying various parameter values, which is solvable simultaneously by a distributed computation algorithm. A reference solution obtained by applying a genetic algorithm is used as an upper bound of the optimal solution, used to reduce the entire search region.