Surrogate-Assisted (1+1)-CMA-ES with Switching Mechanism of Utility Functions
Surrogate-Assisted (1+1)-CMA-ES with Switching Mechanism of Utility Functions
复制标题
具有效用函数切换机制的代理辅助(1 1)-CMA-ES
DOI：
10.1007/978-3-031-30229-9_51
复制
发表时间：
2023
期刊：
影响因子：
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通讯作者：
Shinichi Shirakawa
中科院分区：
文献类型：
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作者：
Yutaro Yamada;Kento Uchida;Shota Saito;Shinichi Shirakawa
目标函数的任何单调递增变换的不变性是协方差矩阵适应进化策略（CMA-ES）的基本属性。然而，代理辅助的 CMA-ES 经常会失去这种不变性，因为代理模型的性能受到这种转换的影响。在本文中，我们提出了一种代理辅助的 CMA-ES，其高斯过程回归（GPR）具有这种转换的鲁棒性。我们引入了两个基于候选解的排名和勒贝格度量的效用函数，它们对于这种变换是不变的。我们使用效用函数值而不是目标函数值来训练 GPR，以估计候选解决方案的排名。此外，我们提出了切换高斯过程CMA-ES（SGP-CMA-ES），它包含一种机制，除了目标函数值之外，还从效用函数值中选择合适的GPR目标变量，以提高GPR可以轻松估计的目标函数的性能。实验结果表明，SGP-CMA-ES在多次变换的目标函数上优于现有方法，同时在未变换的目标函数上保持与现有方法相当的性能。
The invariance to any monotonically increasing transformation of the objective function is an essential property of the covariance matrix adaptation evolution strategy (CMA-ES). However, the surrogate-assisted CMA-ES often loses this invariance because the performance of the surrogate model is influenced by such transformation. In this paper, we propose a surrogate-assisted-CMA-ES with the Gaussian process regression (GPR) possessing the robustness for such transformation. We introduce two utility functions based on the ranking and Lebesgue measure of candidate solutions, which are invariant to such transformation. We train GPR with the utility function values instead of the objective function values to estimate the ranking of the candidate solutions. Moreover, we propose switching Gaussian process CMA-ES (SGP-CMA-ES), which contains a mechanism selecting the suitable target variable of GPR from utility function values in addition to the objective function values to improve the performance on the objective functions that GPR can estimate easily. The experimental results show that SGP-CMA-ES is superior to existing methods on the objective function with several transformations, while maintaining the performance comparable to that of existing methods on the objective function without transformation.