Optimization of simulation-based or data-driven systems is a challenging task, which has attracted significant attention in the recent literature. A very efficient approach for optimizing systems without analytical expressions is through fitting surrogate models. Due to their increased flexibility, nonlinear interpolating functions, such as radial basis functions and Kriging, have been predominantly used as surrogates for data-driven optimization; however, these methods lead to complex nonconvex formulations. Alternatively, commonly used regression-based surrogates lead to simpler formulations, but they are less flexible and inaccurate if the form is not known a priori. In this work, we investigate the efficiency of subset selection regression techniques for developing surrogate functions that balance both accuracy and complexity. Subset selection creates sparse regression models by selecting only a subset of original features, which are linearly combined to generate a diverse set of surrogate models. Five different subset selection techniques are compared with commonly used nonlinear interpolating surrogate functions with respect to optimization solution accuracy, computation time, sampling requirements, and model sparsity. Our results indicate that subset selection-based regression functions exhibit promising performance when the dimensionality is low, while interpolation performs better for higher dimensional problems.

中文翻译：

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基于机器学习的替代模型，用于数据驱动的优化：回归技术子集选择的比较

基于仿真或数据驱动系统的优化是一项艰巨的任务，在最近的文献中引起了极大的关注。在没有解析表达式的情况下优化系统的一种非常有效的方法是通过拟合代理模型。由于它们具有更高的灵活性，因此非线性插值函数（例如径向基函数和Kriging）已主要用作数据驱动优化的替代。然而，这些方法导致复杂的非凸配方。或者，常用的基于回归的替代方法可简化公式，但如果先验形式未知，则它们的灵活性和准确性就会降低。在这项工作中，我们调查了子集选择回归技术开发兼顾准确性和复杂性的替代功能的效率。子集选择通过仅选择原始特征的子集来创建稀疏回归模型，这些原始特征被线性组合以生成多样化的替代模型集。在优化解决方案精度，计算时间，采样要求和模型稀疏性方面，将五种不同的子集选择技术与常用的非线性内插替代函数进行了比较。我们的结果表明，当维数较低时，基于子集选择的回归函数表现出令人鼓舞的性能，而插值对较高维的问题表现更好。在优化解决方案精度，计算时间，采样要求和模型稀疏性方面，将五种不同的子集选择技术与常用的非线性内插替代函数进行了比较。我们的结果表明，当维数较低时，基于子集选择的回归函数表现出令人鼓舞的性能，而插值对较高维的问题表现更好。在优化解决方案精度，计算时间，采样要求和模型稀疏性方面，将五种不同的子集选择技术与常用的非线性内插替代函数进行了比较。我们的结果表明，当维数较低时，基于子集选择的回归函数表现出令人鼓舞的性能，而插值对较高维的问题表现更好。