Sequential Approximate Optimization Using Radial Basis Function Network (Application to the Discrete Design Variable Problems)

Abstract

This paper proposes a Sequential Approximate Optimization (SAO) for the discrete design variable problems using Radial Basis Function (RBF) Network. We consider that there are two important keys for SAO: One is the parameter adjustment for good approximation, and the other is to explore the sparse region for global approximation. The authors have proposed the simple estimate of the width in the Gaussian Kernel for good approximation. In addition, in order to explore the sparse region, we have developed the density function. The density function with the simple estimate of the width works well in the case of the continuous design variables. However, a simple application of the density function to the discrete design variable problems will cause some difficulties. In order to overcome these difficulties and find the sparse region of the discrete design variables with the density function, the new variables for the discrete design variables are introduced. By using the new variables, it is possible to find the sparse region of the discrete design variables. A simple sampling algorithm is shown, in which the Discrete Differential Evolution (DDE) for the discrete design variables is employed. Through typical numerical examples, the validity of proposed approach is examined.