摘要：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.
