New formulations for the Kissing Number Problem

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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 2, 3 and very recently for 4 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 2, 3 and 4 dimensions.

Sergei Kucherenko, Pietro Belotti, Leo Liberti, Ne

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DAM 2007 | Kissing Number Problem | Level Single Linkage | Mathematical Programming Models |

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Added	13 Dec 2010
Updated	13 Dec 2010
Type	Journal
Year	2007
Where	DAM
Authors	Sergei Kucherenko, Pietro Belotti, Leo Liberti, Nelson Maculan

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New formulations for the Kissing Number Problem

DAM 2007 | Kissing Number Problem | Level Single Linkage | Mathematical Programming Models |

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