On the use of a BSP Tree to create local surrogate models

Abstract

In recent years, Evolutionary Algorithms (EAs) have been widely used to solve difficult optimization problems. However, when these problems are expensive (computationally speaking), they can remain intractable even by these approaches. The EA community has effectively used surrogate models to approximate the response of some of these expensive problems with the aim to replace with it some objective function calls. However, in order to have good results, it is important to have an accurate approach. In this regard, most of the existing approaches try to approximate the whole problem (the so-called global model). However, this may not necessary lead to a more accurate approach. The aim of the present paper is to provide a further insight into this matter through the first comparison (to the best of the authors' knowledge) between localand global-surrogate models. We investigate the performance of three different approaches, two of them have been previously used in the specialized literature, while the third is here proposed. After adjusting the single parameter of each approach, we compare their results with respect to the results produced by the global-surrogate model. The validation was performed using six test functions in three different scenarios: low-, medium-and high-dimensional problems. Results indicate our proposed approach is a viable alternative to create local-surrogate models for mediumand high-dimensional problems, while the global-surrogate model is the option for low-dimensional problems.