Optimization techniques for modeling with piecewise-linear functions

Fuente: arXiv
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Main Authors: Dobrovoczki, Péter, Kis, Tamás
Format: Preprint
Published: 2025
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author Dobrovoczki, Péter
Kis, Tamás
author_facet Dobrovoczki, Péter
Kis, Tamás
contents In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand, we describe a simple heuristic to iteratively construct a triangulation with a small number of triangles, while decreasing the error of the piecewise-linear approximation. On the other hand, we extend known techniques for modeling PWLs in MILPs more efficiently than state-of-the-art methods permit. The crux of our method is that the MILP model is a result of solving some hard combinatorial optimization problems, for which we present heuristic algorithms. The effectiveness of our techniques is demonstrated by a series of computational experiments including a short-term hydropower scheduling problem
format Preprint
id arxiv_https___arxiv_org_abs_2503_10405
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimization techniques for modeling with piecewise-linear functions
Dobrovoczki, Péter
Kis, Tamás
Optimization and Control
In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand, we describe a simple heuristic to iteratively construct a triangulation with a small number of triangles, while decreasing the error of the piecewise-linear approximation. On the other hand, we extend known techniques for modeling PWLs in MILPs more efficiently than state-of-the-art methods permit. The crux of our method is that the MILP model is a result of solving some hard combinatorial optimization problems, for which we present heuristic algorithms. The effectiveness of our techniques is demonstrated by a series of computational experiments including a short-term hydropower scheduling problem
title Optimization techniques for modeling with piecewise-linear functions
topic Optimization and Control
url https://arxiv.org/abs/2503.10405