Koetsu Yamazaki

Differential evolution as the global optimization technique and its application to structural optimization

In this paper, the basic characteristics of the differential evolution (DE) are examined. Thus, one is the meta-heuristics, and the other is the global optimization technique. It is said that DE is the global optimization technique, and also belongs to the meta-heuristics. Indeed, DE can find the global minimum through numerical experiments. However, there are no proofs and useful investigations with regard to such comments. In this paper, the DE is compared with the generalized random tunneling algorithm (GRTA) and the particle swarm optimization (PSO) that are the global optimization techniques for continuous design variables. Through the examinations, some common characteristics as the global optimization technique are clarified in this paper. Through benchmark test problems including structural optimization problems, the search ability of DE as the global optimization technique is examined.

Simple estimate of the width in Gaussian kernel with adaptive scaling technique

This paper presents a simple method to estimate the width of Gaussian kernel based on an adaptive scaling technique. The Gaussian kernel is widely employed in radial basis function (RBF) network, support vector machine (SVM), least squares support vector machine (LS-SVM), Kriging models, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an important role. Determination of the optimal width is a time-consuming task. Therefore, it is preferable to determine the width with a simple manner. In this paper, we first examine a simple estimate of the width proposed by Nakayama et al. Through the examination, four sufficient conditions for the simple estimate of the width are described. Then, a new simple estimate for the width is proposed. In order to obtain the proposed estimate of the width, all dimensions are equally scaled. A simple technique called the adaptive scaling technique is also developed. It is expected that the proposed simple method to estimate the width is applicable to wide range of machine learning techniques employing the Gaussian kernel. Through examples, the validity of the proposed simple method to estimate the width is examined.

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

Abstract 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.