Linear, nested, and quadratic ordered measures: Computation and incorporation into optimization problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908280160256000 |
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| author | Blanco, Victor Pozo, Miguel A. Puerto, Justo Torrejon, Alberto |
| author_facet | Blanco, Victor Pozo, Miguel A. Puerto, Justo Torrejon, Alberto |
| contents | In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models allowing their efficient computation. We assess the usefulness of this approach applying it to three different families of measures, namely linear, nested, and quadratic ordered measures. Computational results are reported showing the efficiency and accuracy of our methods as compared with standard implementations in numerical software packages. Finally, we illustrate this methodology by computing a number of optimal solutions with respect to different metrics on three well-known linear and combinatorial optimization problems: scenario analysis in linear programming, the traveling salesman and the weighted multicover set problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear, nested, and quadratic ordered measures: Computation and incorporation into optimization problems Blanco, Victor Pozo, Miguel A. Puerto, Justo Torrejon, Alberto Optimization and Control Discrete Mathematics Computation 90C G.2.0 In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models allowing their efficient computation. We assess the usefulness of this approach applying it to three different families of measures, namely linear, nested, and quadratic ordered measures. Computational results are reported showing the efficiency and accuracy of our methods as compared with standard implementations in numerical software packages. Finally, we illustrate this methodology by computing a number of optimal solutions with respect to different metrics on three well-known linear and combinatorial optimization problems: scenario analysis in linear programming, the traveling salesman and the weighted multicover set problem. |
| title | Linear, nested, and quadratic ordered measures: Computation and incorporation into optimization problems |
| topic | Optimization and Control Discrete Mathematics Computation 90C G.2.0 |
| url | https://arxiv.org/abs/2503.18097 |