Surrogate-assisted evolutionary framework with an ensemble of teaching-learning and differential evolution for expensive optimization

Abstract

Surrogate-Assisted Evolutionary Algorithms (SAEAs) integrate Evolutionary Algorithms (EAs) with surrogate models to reduce the actual number of expensive function evaluations and have been widely used in solving Expensive Optimization Problems (EOPs). However, because of the insufficient diversity of new solutions, SAEAs often fall into local optima and result in evolutionary stagnation when dealing with complex problems. To improve the diversity of new solutions, this paper introduces a Surrogate-Assisted evolutionary Framework with an ensemble of Teaching-learning and Differential evolution (SAF-TD), which successfully integrates the strengths of both EAs to produce more diverse and effective solutions. The main contributions are summarized as follows: First, a novel framework that effectively integrates two distinct EAs using a radial basis function surrogate model and strategic sampling is introduced. Second, a mutation strategy with a supervisory mechanism is proposed to enhance mutation effectiveness and avoid stagnation. Third, a volatility index derived from dimensional improvements is incorporated into parameter control to address fitness-dependent weaknesses. Experiments on five expensive optimization functions and the CEC2017 test suite across multiple dimensions were conducted to evaluate the performance of SAF-TD. The results demonstrate that SAF-TD is highly competitive compared with state-of-the-art SAEAs and exhibits excellent performance in solving EOPs.