Often functional relationships are well known, but they are too complex to be used efficiently in optimization problems like scheduling formulations. Hence the functions are often replaced by data-based surrogate models. Especially, linear models are often used, since they are easier to solve than non-linear ones. The use of piecewise linear surrogate models allows for an improved consideration of nonlinearities. Although, the number of linear elements must be kept small in order not to lose the advantages of a linear-based formulation. In this work, two approaches for generating piecewise linear surrogate models are proposed, whereby the basic idea of both approaches is the determination of a reduced set of data points that provides an appropriate approximation of the original data via multi-dimensional linear interpolation. The approaches differ in their concepts: One is a numerical algorithm, the other an optimization-based technique. In this contribution, these approaches are described and subsequently compared.

通常，功能关系是众所周知的，但是它们过于复杂，无法有效地用于优化问题（如计划制定）。因此，这些功能通常被基于数据的代理模型代替。特别是，由于线性模型比非线性模型更容易求解，因此经常使用线性模型。使用分段线性替代模型可以更好地考虑非线性。虽然，线性元件的数量必须保持较小，以免失去基于线性的配方的优点。在这项工作中，提出了两种生成分段线性替代模型的方法，其中两种方法的基本思想是确定减少的数据点集，该数据点集可通过多维线性插值提供适当的原始数据近似值。这些方法的概念不同：一种是数值算法，另一种是基于优化的技术。在此贡献中，描述了这些方法并随后进行了比较。