An Evolutionary Algorithm Assisted by an Ensemble of Pareto-Optimal Surrogate Models

An ensemble of surrogate models helps improve the prediction quality and robustness of surrogate models, and in turn, the search performance of surrogate-assisted evolutionary algorithms (SAEAs). Although different degrees of smoothness of the approximated fitness landscapes need to be carefully designed for an effective ensemble, little attention has been paid to the explicit tuning of the degree of smoothness derived by surrogate models. This study proposes an adaptive ensemble SAEA, which automatically constructs plausible ensemble models by optimizing their parameter settings. Unlike existing adaptive/ensemble SAEAs, which consider prediction accuracy alone, the proposed algorithm optimizes the structure of radial basis function networks (RBFNs) by solving bi-objective minimization problems of approximation error and model complexity, resulting in robust ensemble models of accurate surrogate models with different degrees of smoothness of the approximated fitness landscapes. As a result, the over/under-fittings are reduced. Additionally, an infill criterion is designed so that surrogate models with different degrees of smoothness can contribute to the solution prescreening. The experimental results demonstrated the statistical superiority of our algorithm over state-of-the-art SAEAs on a single-objective benchmark and real-world problem sets under an expensive optimization scenario. The source code of the proposed algorithm is available at https://github.com/haranychan/EPOS.