Detection of the permutation symmetry in pattern sets

Symmetry is a powerful tool to reduce the freedom degrees of asystem. But the applicability of the symmetry tool stronglydepends on the ability to calculate the symmetries of the system.There exists an interesting algorithmic problem to searchfor the symmetry of a high-dimensional system. In thispaper, a genetic algorithm-based permutation symmetry detectionapproach is proposed for pattern set. Firstly, the permutationsymmetry distance (PSD) is defined to measure the similarity of apattern set before and after being transformed by apermutation operator. Secondly, the permutation symmetry detectionproblem is converted into an optimization problem by taking thePSD as a fitness function. Lastly, a genetic algorithm-basedapproach is designed for the symmetry detection problem. Computersimulation results are also given for five pattern sets ofdifferent dimensionality, which show the efficiency andspeediness of the proposed detection approach, especially inhigh-dimensional cases