On Supportedness in Multi-Objective Combinatorial Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909767577894912 |
|---|---|
| author | Könen, David Stiglmayr, Michael |
| author_facet | Könen, David Stiglmayr, Michael |
| contents | This paper addresses an inconsistency in various definitions of supported non-dominated points within multi-objective combinatorial problems (MOCO). MOCO problems are known to contain supported and unsupported non-dominated points, with the latter typically outnumbering the former. Supported points are, in general, easier to determine, can serve as representations, and are used in two-phase methods to generate the entire non-dominated point set. Despite their importance, several different characterizations for supported efficient solutions (and supported non-dominated points) are used in the literature.
While these definitions are equivalent for multi-objective linear problems, they can yield different sets of supported non-dominated points for MOCO problems. We show by an example that these definitions are not equivalent for MOCO or general multi-objective optimization problems. Moreover, we analyze the structural and computational properties of the resulting sets of supported non-dominated points. These considerations motivate us to summarize equivalent definitions and characterizations for supported efficient solutions and to introduce a distinction between supported and weakly supported efficient solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Supportedness in Multi-Objective Combinatorial Optimization Könen, David Stiglmayr, Michael Optimization and Control Discrete Mathematics This paper addresses an inconsistency in various definitions of supported non-dominated points within multi-objective combinatorial problems (MOCO). MOCO problems are known to contain supported and unsupported non-dominated points, with the latter typically outnumbering the former. Supported points are, in general, easier to determine, can serve as representations, and are used in two-phase methods to generate the entire non-dominated point set. Despite their importance, several different characterizations for supported efficient solutions (and supported non-dominated points) are used in the literature. While these definitions are equivalent for multi-objective linear problems, they can yield different sets of supported non-dominated points for MOCO problems. We show by an example that these definitions are not equivalent for MOCO or general multi-objective optimization problems. Moreover, we analyze the structural and computational properties of the resulting sets of supported non-dominated points. These considerations motivate us to summarize equivalent definitions and characterizations for supported efficient solutions and to introduce a distinction between supported and weakly supported efficient solutions. |
| title | On Supportedness in Multi-Objective Combinatorial Optimization |
| topic | Optimization and Control Discrete Mathematics |
| url | https://arxiv.org/abs/2501.13842 |