Efficient Surrogate Model Assisted Estimation of Distribution Algorithm for Expensive Optimization

Abstract

In recent years, several surrogate assisted evolutionary algorithms (SAEAs) have been proposed to solve expensive optimization problems. These problems lack explicit expressions and are characterized by high invocation costs. SAEAs leverage surrogate models to accelerate convergence towards the optimal region and reduce the number of function evaluations. While Gaussian Processes (GPs) are widely used due to their robustness and capability of providing uncertainty estimates, their applicability becomes limited in scenarios involving a large number of samples or high-dimensional spaces. This is due to their cubic time complexity in relation to the number of samples, which results in prohibitive computational demands for large-scale problems. To address the challenge, this work presents an efficient surrogate model-assisted estimation of the distribution algorithm (ESAEDA). This method employs a random forest as a surrogate model and combines it with a GP-hedge acquisition strategy to ensure the efficiency and accuracy of model-assisted selection. An improved EDA model called the variable-width histogram model with some unevaluated solutions is used to generate new solutions. To demonstrate the benefits of the proposed method, we compared ESAEDA with several state-of-the-art surrogate-assisted evaluation algorithms and the Bayesian optimization method. Experimental results demonstrate the superiority of the proposed algorithm over these comparison algorithms for two well-known test suites.