Global Optimization Method to Locate Multiple Local Optima with Response Surface Approximation Methodology

Abstract

A considerable number of functional evaluations may be required in the process of optimization. Although approximation models constructed by response surface methodology can significantly reduce functional evaluations, the design accuracy may be strongly dependent on the type of activation functions and designs used. In this paper, we propose techniques to search the design space containing the global optimal design using designs by conditioned random seeds, and techniques for determining more accurate approximations by employing a sequential approach called the most probable optimal design (MPOD) method. The MPOD method is a response surface methodology based on the holographic neural network, which uses the exponential function as an activation function. In the MPOD method, extrapolation is employed to make the technique available for general application in structural optimization. The formula to estimate the necessary functional evaluations under certain conditions is expressed. Application examples show that the MPOD method is an effective methodology, which is expected to determine the optimal design with multiple local optima.