A Decision-Making Method in Polyhedral Convex Set Optimization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909327232598016 |
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| author | Löhne, Andreas |
| author_facet | Löhne, Andreas |
| contents | Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on an ordering relation on a family of sets. When faced with multiple optimizers, a decision maker must choose one. Visualizing the values associated with these optimizers could provide a solid basis for decision-making. However, these values are sets, making it challenging to visualize many of them. Therefore, we propose a method where an optimizer is selected by designing the respective outcome set through a trial-and-error process. In a polyhedral convex setting, we discuss an implementation and prove that an optimizer can be found using this method after a finite number of design steps. We motivate the problem setting and illustrate the process using an example: a two-stage bi-objective network flow problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Decision-Making Method in Polyhedral Convex Set Optimization Löhne, Andreas Optimization and Control 90C29, 90B50, 90B10 Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on an ordering relation on a family of sets. When faced with multiple optimizers, a decision maker must choose one. Visualizing the values associated with these optimizers could provide a solid basis for decision-making. However, these values are sets, making it challenging to visualize many of them. Therefore, we propose a method where an optimizer is selected by designing the respective outcome set through a trial-and-error process. In a polyhedral convex setting, we discuss an implementation and prove that an optimizer can be found using this method after a finite number of design steps. We motivate the problem setting and illustrate the process using an example: a two-stage bi-objective network flow problem. |
| title | A Decision-Making Method in Polyhedral Convex Set Optimization |
| topic | Optimization and Control 90C29, 90B50, 90B10 |
| url | https://arxiv.org/abs/2409.17998 |