The radial basis function (RBF) model and the Kriging model have been widely used in the surrogate-assisted evolutionary algorithms (SAEAs). Based on their characteristics, a global and local surrogate-assisted differential evolution algorithm (GL-SADE) for high-dimensional expensive problems is proposed in this article, in which a global RBF model is trained with all samples to estimate a global trend, and then its optima is used to significantly accelerate the convergence process. A local Kriging model prefers to select points with good predicted fitness and great uncertainty, which can effectively prevent the search from getting trapped into local optima. When the local Kriging model finds the best solution so far, a reward search strategy is executed to further exploit the local Kriging model. The experiments on a set of benchmark functions with dimensions varying from 30 to 200 are conducted to evaluate the performance of the proposed algorithm. The experimental results of the proposed algorithm are compared to four state-of-the-art algorithms to show its effectiveness and efficiency in solving high-dimensional expensive problems. Besides, GL-SADE is applied to an airfoil optimization problem to show its effectiveness.

中文翻译：

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一种解决高维昂贵优化问题的代理辅助差分进化算法


径向基函数（RBF）模型和克里金模型已广泛应用于代理辅助进化算法（SAEA）中。基于它们的特点，本文提出了一种针对高维昂贵问题的全局和局部代理辅助差分进化算法（GL-SADE），其中用所有样本训练全局RBF模型来估计全局趋势，并且然后它的最优值被用来显着加速收敛过程。局部克里金模型更倾向于选择预测适应度好、不确定性大的点，可以有效防止搜索陷入局部最优。当局部克里金模型找到迄今为止最好的解决方案时，将执行奖励搜索策略以进一步利用局部克里金模型。在一组维度从 30 到 200 不等的基准函数上进行实验，以评估所提出算法的性能。该算法的实验结果与四种最先进的算法进行了比较，以显示其在解决高维昂贵问题方面的有效性和效率。此外，GL-SADE被应用于翼型优化问题，显示了其有效性。