TY - JOUR

T1 - Generation of linear-based surrogate models from non-linear functional relationships for use in scheduling formulation

AU - Obermeier, Andreas

AU - Vollmer, Nikolaus

AU - Windmeier, Christoph

AU - Esche, Erik

AU - Repke, Jens-Uwe

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Data-based surrogate models

KW - Piecewise linear

KW - Data reduction

U2 - 10.1016/j.compchemeng.2020.107203

DO - 10.1016/j.compchemeng.2020.107203

M3 - Journal article

SN - 0098-1354

VL - 146

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

M1 - 107203

ER -