Circular chains of chinese dice
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| Autoři: | , |
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| Médium: | artículo original |
| Stav: | Versión publicada |
| Datum vydání: | 2010 |
| Popis: | In this paper we study Chinese dice, mathematical objects similar to ordinary dice but allowing repetition among their face values. We say that a die A is preferred over a die B (written A > B) if A wins more frequently than B does. We study first the existence of circular chains of three dice A, B, C (those that A > B > C > A) using a mixed integer programming algorithm. Then we generalize the problem to n-dimensional dice—that is, dice of n faces, with n ≥ 4—and we search circular chains of length m (with m ≥ 3) using a simulated annealing algorithm. We compare some different objective functions and obtain good solutions to the problem with very efficient algorithms. Finally we obtain a theoretical result concerning the existence of circular chains in the general case. |
| Země: | Portal de Revistas UCR |
| Instituce: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Jazyk: | Español |
| OAI Identifier: | oai:portal.ucr.ac.cr:article/312 |
| On-line přístup: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/312 |
| Klíčové slovo: | Chinese dice mixed-integer programming simulated annealing combinatorial optimization Dados chinos programación entera mixta sobrecalentamiento simulado recocido simulado optimización combinatoria |