A heuristic search algorithm for discovering large Condorcet domains
arxiv(2023)
摘要
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.
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