EURO 2024 Copenhagen
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723. A heuristic for fitting piecewise-linear models of bivariate functions with simplices and its application to an industrial use case

Invited abstract in session WC-19: OR in Energy II, stream OR in Energy.

Wednesday, 12:30-14:00
Room: 44 (building: 116)

Authors (first author is the speaker)

1. Victor Ruela
Institute of Energy Systems and Thermodynamics, TU Wien
2. Paul van Beurden
Ceramics Research Centre, Tata Steel Nederland
3. René Hofmann
Institute for Energy Systems and Thermodynamics, TU Wien
4. Felix Birkelbach
Institute of Energy Systems and Thermodynamics, TU Wien

Abstract

A common approach to solving MINLP problems is to convert them to a MILP using piecewise-linear (PWL) models to approximate the nonlinearities. However, finding a PWL approximation that respects an error tolerance with the minimum number of linear pieces is a challenging task. Moreover, available methods are complicated and difficult to implement. This paper addresses finding error-bounded PWL approximations for continuous and smooth bivariate functions. The method proposed is an easy-to-implement heuristic applied for the case of a triangulation generated over rectangular grids. On each iteration, a nonlinear programming problem is solved to adjust the placement of the linear pieces to minimize the approximation error. Then, we increase the number of breakpoints for the variable with maximum error reduction potential. For an industrial use case from the steelmaking industry, the ladle dispatching problem with refractory temperature control, we show how applying this heuristic can reduce the complexity of the resulting MILP while respecting a strict approximation error requirement. The heuristic achieved an average reduction of 67% in the solution time of the MILP with an average 34% reduction in the approximation error.

Keywords

Status: accepted

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