Generation of linear-based surrogate models from non-linear functional relationships for use in scheduling formulation

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.