Optimization techniques for modeling with piecewise-linear functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918344178794496 |
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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 |
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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 |