A heuristic search algorithm for discovering large Condorcet domains
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911351045095424 |
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| author | Zhou, Bei Riis, Søren |
| author_facet | Zhou, Bei Riis, Søren |
| contents | The study of large Condorcet domains (CD) has been a significant area of interest in voting theory. In this paper, our goal is to search for large CDs that are hitherto unknown. With a straightforward combinatorial definition, searching for large CDs is naturally suited for algorithmic optimisations. For each value of n>2, one can ask for the size of the largest CD, thus finding the largest CDs provides an important benchmark for heuristic-based combinatorial optimisation algorithms. Despite extensive research over the past three decades, the CD sizes identified in 1996 remain the best known for many values of n. When n>8, conducting an exhaustive search becomes computationally unfeasible, thereby prompting the use of heuristic methods. To address this, we developed a novel heuristic search algorithm in which a specially designed heuristic function, backed by a lookup database, directs the search towards promising branches in the search tree. Our algorithm found new large CDs of size 1082 (surpassing the previous record of 1069) for n=10, and 2349 (improving the previous 2324) for n=11. Notably, these newly discovered CDs exhibit characteristics distinct from those of known CDs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06524 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A heuristic search algorithm for discovering large Condorcet domains Zhou, Bei Riis, Søren Discrete Mathematics The study of large Condorcet domains (CD) has been a significant area of interest in voting theory. In this paper, our goal is to search for large CDs that are hitherto unknown. With a straightforward combinatorial definition, searching for large CDs is naturally suited for algorithmic optimisations. For each value of n>2, one can ask for the size of the largest CD, thus finding the largest CDs provides an important benchmark for heuristic-based combinatorial optimisation algorithms. Despite extensive research over the past three decades, the CD sizes identified in 1996 remain the best known for many values of n. When n>8, conducting an exhaustive search becomes computationally unfeasible, thereby prompting the use of heuristic methods. To address this, we developed a novel heuristic search algorithm in which a specially designed heuristic function, backed by a lookup database, directs the search towards promising branches in the search tree. Our algorithm found new large CDs of size 1082 (surpassing the previous record of 1069) for n=10, and 2349 (improving the previous 2324) for n=11. Notably, these newly discovered CDs exhibit characteristics distinct from those of known CDs. |
| title | A heuristic search algorithm for discovering large Condorcet domains |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2303.06524 |