On Nonstationary Gaussian Process Model for Solving Data-Driven Optimization Problems
研究发现优化问题中的高斯过程大多是非平稳的，提出用非平稳高斯过程作为代理模型，在基准问题和天线设计问题上验证了其优于传统平稳模型。
In data-driven evolutionary optimization, most existing Gaussian processes (GPs)-assisted evolutionary algorithms (EAs) adopt stationary GPs (SGPs) as surrogate models, which might be insufficient for solving most optimization problems. This article finds that GPs in the optimization problems are nonstationary with great probability. We propose to employ a nonstationary GP (NSGP) surrogate model for data-driven evolutionary optimization, where the mean of the NSGP is allowed to vary with the decision variables, while its residue variance follows an SGP. In this article, the nonstationarity of GPs in the tested functions is theoretically analyzed. In addition, this article constructs an NSGP where the SGP is a degenerate case. Performance comparisons of the NSGP with the SGP and the NSGP-assisted EA (NSGP-MAEA) with the SGP-assisted EA (SGP-MAEA) are carried out on a set of benchmark problems and an antenna design problem. These comparison results demonstrate the competitiveness of the NSGP model.