An extension of Ordered Weighted Averaging over intervals with application to optimization under risk
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912867251388416 |
|---|---|
| author | Baak, Werner Goerigk, Marc Kasperski, Adam Zieliński, Paweł |
| author_facet | Baak, Werner Goerigk, Marc Kasperski, Adam Zieliński, Paweł |
| contents | The Ordered Weighted Averaging (OWA) operator is a traditional and commonly used criterion for aggregating discrete values of uncertain quantities. In this paper, it is shown that the discrete OWA naturally extends to the continuous case by using the concept of a distortion risk measure. It is shown how to apply the distortion risk measure to optimization problems with a linear objective function, whose coefficients are random variables with continuous distribution functions supported on intervals. The case where these coefficients are independent, uniformly distributed random variables is explored in more detail. The computational complexity of the resulting optimization problem is analyzed, and solution methods with approximation guarantees are proposed. These methods are also verified through computational experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An extension of Ordered Weighted Averaging over intervals with application to optimization under risk Baak, Werner Goerigk, Marc Kasperski, Adam Zieliński, Paweł Optimization and Control The Ordered Weighted Averaging (OWA) operator is a traditional and commonly used criterion for aggregating discrete values of uncertain quantities. In this paper, it is shown that the discrete OWA naturally extends to the continuous case by using the concept of a distortion risk measure. It is shown how to apply the distortion risk measure to optimization problems with a linear objective function, whose coefficients are random variables with continuous distribution functions supported on intervals. The case where these coefficients are independent, uniformly distributed random variables is explored in more detail. The computational complexity of the resulting optimization problem is analyzed, and solution methods with approximation guarantees are proposed. These methods are also verified through computational experiments. |
| title | An extension of Ordered Weighted Averaging over intervals with application to optimization under risk |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2410.09786 |