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Mathematical Problems in Engineering
Volume 2014, Article ID 657170, 16 pages
Research Article

A Quasiphysical and Dynamic Adjustment Approach for Packing the Orthogonal Unequal Rectangles in a Circle with a Mass Balance: Satellite Payload Packing

1School of Information and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China
2School of Mathematics and Computer Science, Xiangtan University, Xiangtan, Hunan 411105, China
3Department of Aeronautics, Xiamen University, Xiamen, Fujian 361005, China

Received 2 June 2014; Revised 28 August 2014; Accepted 22 September 2014; Published 2 December 2014

Academic Editor: Oleg V. Gendelman

Copyright © 2014 Ziqiang Li 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 orthogonal unequal rectangles in a circle with a mass balance (BCOURP) is a typical combinational optimization problem with the NP-hard nature. This paper proposes an effective quasiphysical and dynamic adjustment approach (QPDAA). Two embedded degree functions between two orthogonal rectangles and between an orthogonal rectangle and the container are defined, respectively, and the extruded potential energy function and extruded resultant force formula are constructed based on them. By an elimination of the extruded resultant force, the dynamic rectangle adjustment, and an iteration of the translation, the potential energy and static imbalance of the system can be quickly decreased to minima. The continuity and monotony of two embedded degree functions are proved to ensure the compactness of the optimal solution. Numerical experiments show that the proposed QPDAA is superior to existing approaches in performance.