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...

Descripción completa

Detalles Bibliográficos
Autores: Ruiz de Angulo García, Vicente|||0000-0002-2067-7399, Torras, Carme|||0000-0002-2933-398X
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
Descripción
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.