A Novel Evolutionary Sampling Assisted Optimization Method for High-Dimensional Expensive Problems

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for solving high-dimensional expensive problems. The basic idea of SAEAs is the integration of nature-inspired searching ability of evolutionary algorithms and prediction ability of surrogate models. This paper proposes a novel evolutionary sampling assisted optimization (ESAO) method which combines the two abilities to consider global exploration and local exploitation. Differential evolution is employed to generate offspring using mutation and crossover operators. A global radial basis functions surrogate model is built for prescreening of the offspring’s objective function values and identifying the best one, which will be evaluated with the true function. The best offspring will replace its parent’s position in the population if its function value is smaller than that of its parent. A local surrogate model is then built with selected current best solutions. An optimizer is applied to find the optimum of the local model. The optimal solution is then evaluated with the true function. Besides, a better point found in the local search will be added into the population in the global search. Global and local searches will alternate if one search cannot lead to a better solution. Comprehensive analysis is conducted to study the mechanism of ESAO and insights are gained on different local surrogates. The proposed algorithm is compared with two state-of-the-art SAEAs on a series of high-dimensional problems and results show that ESAO behaves better both in effectiveness and robustness on most of the test problems. Besides, ESAO is applied to an airfoil optimization problem to show its effectiveness.