Expensive Optimization Based on Evolutionary Multi-Tasking and Hybrid Restart Strategy

Evolutionary Algorithms (EAs) can not handle expensive optimization problems (EOPs) well due to the limited function evaluations in EOPs. To address this challenge, surrogate-assisted evolutionary algorithms (SAEAs) have been widely used and obtained good performance. With the problem dimension increases, SAEAs encounter some challenges in relatively high complexity on the training time and prediction time. To address this, this article proposes a novel expensive optimization algorithm with evolutionary multi-tasking and hybrid restart strategy (HRS-EMT). In the surrogate model construct, two radial basis function (RBF) models with different kernel functions are trained on all evaluated data to provide diversity and then are solved by a multi-tasking optimizer to a better optimization performance. In the surrogate model management, HRS-EMT combines multiple RBF models into an ensemble RBF (ERBF) model, strategically applied in the initial population pre-selection of surrogate model. Based on the prediction of ERBF surrogate model, HRS-EMT can obtain a better initial population in high dimensions. HRS-EMT is validated on twelve benchmark functions and compared with other state-of-the-art SAEAs. Experimental studies have shown the superior or comparable performance to other popular SAEAs in addressing EOPs.