Exploiting single-cycle symmetries in branch-and-prune algorithms
As a first attempt to exploit symmetries in continuous con- straint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a Branch-and-Prune algorithm without interfering with it. A key c...
| Autores: | , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2674 |
| Acceso en línea: | https://hdl.handle.net/2117/2674 |
| Access Level: | acceso abierto |
| Palabra clave: | Automation Robots -- Kinematics Automatització Robots Cinemàtica Classificació INSPEC::Automation Classificació INSPEC::Automation::Robots::Robot kinematics Àrees temàtiques de la UPC::Informàtica::Automàtica i control Àrees temàtiques de la UPC::Informàtica::Robòtica |
| Sumario: | As a first attempt to exploit symmetries in continuous con- straint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of n. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and a kinematics solver are used to show the performance of the approach in practice. |
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