Multiobjective Optimization under Uncertainties using Conditional Pareto Fronts
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917203551453184 |
|---|---|
| author | Trappler, Victor Helbert, Céline Riche, Rodolphe Le |
| author_facet | Trappler, Victor Helbert, Céline Riche, Rodolphe Le |
| contents | In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define the probability of coverage of the Conditional Pareto Set which can be interpreted as the probability for a design to be optimal in the Pareto sense. Due to the computational cost of such an approach, we introduce an Active Learning method based on Gaussian Process Regression in order to improve the estimation of this probability, which relies on a reformulation of the EHVI. We illustrate those methods on a few toy problems of moderate dimension, and on the problem of designing a cabin to highlight the differences in solutions brought by different formulations of the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiobjective Optimization under Uncertainties using Conditional Pareto Fronts Trappler, Victor Helbert, Céline Riche, Rodolphe Le Optimization and Control In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define the probability of coverage of the Conditional Pareto Set which can be interpreted as the probability for a design to be optimal in the Pareto sense. Due to the computational cost of such an approach, we introduce an Active Learning method based on Gaussian Process Regression in order to improve the estimation of this probability, which relies on a reformulation of the EHVI. We illustrate those methods on a few toy problems of moderate dimension, and on the problem of designing a cabin to highlight the differences in solutions brought by different formulations of the problem. |
| title | Multiobjective Optimization under Uncertainties using Conditional Pareto Fronts |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.04944 |