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Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 81503, 12 pages

Detection of the permutation symmetry in pattern sets

1Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
2National Key Lab for Radar Signal Processing, Xidian University, Xi'an, Shaanxi 710071, China
3School of Computer Science and Technology, Xidian University, Xi'an, Shaanxi 710071, China

Received 19 February 2006; Accepted 1 May 2006

Copyright © 2006 Dong Ji-Yang and Zhang Jun-Ying. 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.


Symmetry is a powerful tool to reduce the freedom degrees of a system. But the applicability of the symmetry tool strongly depends on the ability to calculate the symmetries of the system. There exists an interesting algorithmic problem to search for the symmetry of a high-dimensional system. In this paper, a genetic algorithm-based permutation symmetry detection approach is proposed for pattern set. Firstly, the permutation symmetry distance (PSD) is defined to measure the similarity of a pattern set before and after being transformed by a permutation operator. Secondly, the permutation symmetry detection problem is converted into an optimization problem by taking the PSD as a fitness function. Lastly, a genetic algorithm-based approach is designed for the symmetry detection problem. Computer simulation results are also given for five pattern sets of different dimensionality, which show the efficiency and speediness of the proposed detection approach, especially in high-dimensional cases.