ROBBO: An Efficient Method for Pareto Front Estimation with Guaranteed Accuracy
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912444244295680 |
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| author | Boffadossi, Roberto Leonesio, Marco Fagiano, Lorenzo |
| author_facet | Boffadossi, Roberto Leonesio, Marco Fagiano, Lorenzo |
| contents | A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite, pre-computed number of PF points. Upon termination, it guarantees that the worst-case approximation error lies within a desired tolerance range, predefined by the decision maker, for each of the two objective functions. Theoretical results are derived, about the worst-case number of PF samples required to guarantee the wanted accuracy, both in general and for specific sampling methods from the literature. A comparative analysis, both theoretical and numerical, demonstrates the superiority of the proposed method with respect to popular ones. The approach is finally showcased in a constrained path-following problem for a 2-axis positioning system and in a steady-state optimization problem for a Continuous-flow Stirred Tank Reactor. An open demo implementation of ROBBO is made available online. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ROBBO: An Efficient Method for Pareto Front Estimation with Guaranteed Accuracy Boffadossi, Roberto Leonesio, Marco Fagiano, Lorenzo Optimization and Control Systems and Control A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite, pre-computed number of PF points. Upon termination, it guarantees that the worst-case approximation error lies within a desired tolerance range, predefined by the decision maker, for each of the two objective functions. Theoretical results are derived, about the worst-case number of PF samples required to guarantee the wanted accuracy, both in general and for specific sampling methods from the literature. A comparative analysis, both theoretical and numerical, demonstrates the superiority of the proposed method with respect to popular ones. The approach is finally showcased in a constrained path-following problem for a 2-axis positioning system and in a steady-state optimization problem for a Continuous-flow Stirred Tank Reactor. An open demo implementation of ROBBO is made available online. |
| title | ROBBO: An Efficient Method for Pareto Front Estimation with Guaranteed Accuracy |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2506.18004 |