A Gaussian Process Surrogate Model Assisted Evolutionary Algorithm for Medium Scale Expensive Optimization Problems

TLDR

Surrogate model assisted evolutionary algorithms are increasingly used for computationally expensive optimization, yet most research focuses on small-scale problems and medium-scale (20–50 variables) cases remain underexplored. This study proposes and investigates a Gaussian process surrogate model assisted evolutionary algorithm (GPEME) tailored for medium-scale expensive optimization. GPEME combines a surrogate-model–aware search that focuses on promising regions when high-quality surrogates are hard to build, with Sammon mapping to reduce dimensionality, and a coordinated framework that integrates surrogate modeling and evolutionary search. Experiments on benchmark problems with 20, 30, and 50 variables and a 17-variable power amplifier design problem demonstrate that GPEME achieves high efficiency and effectiveness, yielding better or comparable solutions to three state-of-the-art SAEAs while reducing exact function evaluations by 12% to 50%.

Abstract

Surrogate model assisted evolutionary algorithms (SAEAs) have recently attracted much attention due to the growing need for computationally expensive optimization in many real-world applications. Most current SAEAs, however, focus on small-scale problems. SAEAs for medium-scale problems (i.e., 20-50 decision variables) have not yet been well studied. In this paper, a Gaussian process surrogate model assisted evolutionary algorithm for medium-scale computationally expensive optimization problems (GPEME) is proposed and investigated. Its major components are a surrogate model-aware search mechanism for expensive optimization problems when a high-quality surrogate model is difficult to build and dimension reduction techniques for tackling the “curse of dimensionality.” A new framework is developed and used in GPEME, which carefully coordinates the surrogate modeling and the evolutionary search, so that the search can focus on a small promising area and is supported by the constructed surrogate model. Sammon mapping is introduced to transform the decision variables from tens of dimensions to a few dimensions, in order to take advantage of Gaussian process surrogate modeling in a low-dimensional space. Empirical studies on benchmark problems with 20, 30, and 50 variables and a real-world power amplifier design automation problem with 17 variables show the high efficiency and effectiveness of GPEME. Compared to three state-of-the-art SAEAs, better or similar solutions can be obtained with 12% to 50% exact function evaluations.