Hierarchical Response Surface Methodology for Parameter Optimization: Efficiency of a Hierarchical RSM with a Hessian Matrix

Abstract

We propose a hierarchical response surface methodology (hRSM) for parameter optimization. In this hRSM, a target domain is subdivided recursively based on the coefficient of determination (COD). However, deciding whether to execute subdivision based only on the COD results in a time-consuming technique. To solve this problem, we implemented hRSM with a Hessian matrix (hRSM-Hm) to determine whether a target domain is to be subdivided. To evaluate our proposed technique, we compared hRSM-Hm with a genetic algorithm (GA) in terms of computation time by using various numerical functions. From the results, the hRSM-Hm reduced the computation time by 25% compared with the GA on some functions. If the approximated shape of a function is similar to a quadric surface, even though there are many local minima, the hRSM-Hm could find an optimal set of parameters with very few computational cycles.