Symmetry is a powerful tool to reduce the number of degrees of freedom of a problem.But calculating the symmetry of a high-dimensional system would be very difficult since the total number of transformations increases dramatically with the dimension of the system

which places many restrictions on the application of the symmetry method.A novel approach based on genetic algorithms is proposed to search for the permutation symmetries of the weight matrix of full-connected neural networks within the symmetry group

S

n

.Searching results for several different dimensional matrixes are given and compared to that of the ergodic searching method.It turns out that the searching method based on genetic algorithms can find the majority of symmetric permutations of the matrix within a short time

which mak

es it possible to study and design of the high-dimensional neural networks by the symmetry tool.