By remarkably reducing real fitness evaluations, surrogate-assisted evolutionary algorithms (SAEAs), especially hierarchical SAEAs, have been shown to be effective in solving computationally expensive optimization problems. The success of hierarchical SAEAs mainly profits from the potential benefit of their global surrogate models known as “blessing of uncertainty” and the high accuracy of local models. However, their performance leaves room for improvement on high-dimensional problems since now it is still challenging to build accurate enough local models due to the huge solution space. Directing against this issue, this study proposes a new hierarchical SAEA by training local surrogate models with the help of the random projection technique. Instead of executing training in the original high-dimensional solution space, the new algorithm first randomly projects training samples onto a set of low-dimensional subspaces, then trains a surrogate model in each subspace, and finally achieves evaluations of candidate solutions by averaging the resulting models. Experimental results on seven benchmark functions of 100 and 200 dimensions demonstrate that random projection can significantly improve the accuracy of local surrogate models and the new proposed hierarchical SAEA possesses an obvious edge over state-of-the-art SAEAs.

通过显着减少实际适应度评估，代理辅助进化算法 (SAEA)，尤其是分层 SAEA，已被证明可有效解决计算成本高的优化问题。分层 SAEA 的成功主要得益于其被称为“不确定性的祝福”的全球替代模型的潜在好处和局部模型的高精度。然而，它们的性能为高维问题留下了改进空间，因为现在由于巨大的解决方案空间，构建足够准确的局部模型仍然具有挑战性。针对这个问题，本研究通过在随机投影技术的帮助下训练局部代理模型，提出了一种新的分层 SAEA。而不是在原来的高维解空间中执行训练，新算法首先将训练样本随机投影到一组低维子空间上，然后在每个子空间中训练一个代理模型，最后通过对结果模型进行平均来实现对候选解的评估。在 100 和 200 维的七个基准函数上的实验结果表明，随机投影可以显着提高局部代理模型的准确性，并且新提出的分层 SAEA 比最先进的 SAEA 具有明显的优势。