A uniform sampling method for permutation space

Uniform sampling in the permutation space is very important for solving permutation problems with NP-hard nature. However, due to the complexity of this space, there is no uniform sampling method for it up to now. In this paper, the description of permutation space and a review of uniform sampling in other space are given. After that, the limitation of the random method for uniform sampling is analyzed, and a k-means clustering algorithm with an improved Borda's method is introduced for sampling based on the above analysis. An extended Latin matrix is defined, and a sampling method based on this matrix that can only solve for a fixed number of sampling is presented. The properties of this method are explored and demonstrated. A uniform sampling method is then proposed for an arbitrary number of sampling points. Experiments are implemented under different sizes of permutation spaces and the results show that the method proposed in this paper has superior performance, which is more than 100 times better than the random method.