Sequential approximate optimization for discrete design variable problems using radial basis function network

This paper proposes a sequential approximate optimization (SAO) for discrete design variable problems using radial basis function (RBF) network. We assume that there are two important factors for successful SAO: one is parameter adjustment for good approximation, and the other is to find the unexplored regions for global approximation. The authors propose a simple estimate of the width in the Gaussian kernel for good approximation. In addition, in order to find the unexplored region, we develop a density function that, with the simple estimate of the width, works well in the case of continuous design variables. However, a simple application of the density function to discrete design variables often leads to the wrong result. In order to find the unexplored region of the discrete design variables with our density function, the permutation number is introduced. The density function with the permutation number can find out the unexplored region. As the result, the discrete optimum can find with a small number of function evaluations. The validity of proposed approach is examined by studying typical numerical examples.