Result: New formulations for the Kissing Number Problem
Title:
New formulations for the Kissing Number Problem
Authors:
Source:
3rd Cologne/Twente Workshop on Graphs and Combinatorial OptimizationDiscrete applied mathematics. 155(14):1837-1841
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Plans d'expériences et configurations, Designs and configurations, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Algorithme, Algorithm, Algoritmo, Calcul 2 dimensions, Two-dimensional calculations, Calcul 3 dimensions, Three-dimensional calculations, Combinatoire, Combinatorics, Combinatoria, Garnissage, Packing, Relleno, Informatique théorique, Computer theory, Informática teórica, Liaison génétique, Genetic linkage, Ligamiento genético, Maximum, Máximo, Modèle mathématique, Mathematical model, Modelo matemático, Modèle non linéaire, Non linear model, Modelo no lineal, Méthode optimisation, Optimization method, Método optimización, Méthode stochastique, Stochastic method, Método estocástico, Programmation mathématique, Mathematical programming, Programación matemática, Programmation non linéaire, Non linear programming, Programación no lineal, Programmation stochastique, Stochastic programming, Programación estocástica, Quartier voisinage, Residential neighborhoods, Barrio vecindad, Sphère, Sphere, Esfera, 05B40, 49XX, 65Kxx, 68Wxx, Optimisation stochastique, Global optimization, Multi-level Single Linkage, NLP, Sphere packing, Stochastic algorithm, Variable Neighbourhood Search
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
CPSE, Imperial College, SW7 2AZ London, United Kingdom
Tepper School of Business, Carnegie Mellon University, Pittsburgh PA 15213, United States
LIX, École Polytechnique, Palaiseau 91128, France
COPPE, Universidade Federal do Rio de Janeiro, P.O. Box 68511, 21941-972 Rio de Janeiro, Brazil
Tepper School of Business, Carnegie Mellon University, Pittsburgh PA 15213, United States
LIX, École Polytechnique, Palaiseau 91128, France
COPPE, Universidade Federal do Rio de Janeiro, P.O. Box 68511, 21941-972 Rio de Janeiro, Brazil
ISSN:
0166-218X
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Mathematics
Accession Number:
edscal.19046565
Database:
PASCAL Archive
Further Information
Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for two, three and very recently for four dimensions. We present two nonlinear (nonconvex) mathematical programming models for the solution of the KNP. We solve the problem by using two stochastic global optimization methods: a Multi Level Single Linkage algorithm and a Variable Neighbourhood Search. We obtain numerical results for two, three and four dimensions.