Fast simulated annealing with a multivariate Cauchy distribution and the configuration’s initial temperature

Abstract

We propose a multi-dimensional fast simulated annealing method based on a multivariate Cauchy probability distribution and an initial temperature estimated from the configuration’s variation. While conventional multi-dimensional fast simulated annealing adopts the product of onedimensional random variables generated by a univariate Cauchy distribution, the proposed method generates a random vector from a multivariate Cauchy distribution. In this way, fast simulated annealing for a multi-dimensional problem maintains the same annealing schedule as that for the one-dimensional case. The proposed method also utilizes the initial temperature estimated from the configuration’s variation to generate a candidate state in addition to the conventional initial temperature derived from the variation of the objective function for the acceptance probability. The proposed method is shown not only to guarantee a fast annealing schedule but also to enhance the search capability. The proposed method was tested against the optimization of real-valued functions. We empirically found that the configuration’s initial temperature, together with multivariate Cauchy distribution, is more suitable than the conventional scheme for a fast annealing schedule. Moreover, the proposed method outperforms the conventional one in optimization problems having many variables.