n-dimensional Cauchy neighbor generation for the fast simulate dannealing

Many simulated annealing algorithms use the Cauchy neighbors for fast convergence, and the conventional method uses the product of n one-dimensional Cauchy distributions as an approximation. However, this method slows down the search severely as the dimension gets high because of the dimension-wise neighbor generation. In this paper, we analyze the orthogonal neighbor characteristics of the conventional method and propose a method of generating symmetric neighbors from the n-dimensional Cauchy distribution. The simulation results show that the proposed method is very effective for the search in the simulated annealing and can be applied to many other stochastic optimization algorithms.