New formulations for the Kissing Number Problem

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.

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Sergei Kucherenko, Pietro Belotti, Leo Liberti, Nelson Maculan
• Keywords: DAM 2007, Kissing Number Problem, Level Single Linkage, Mathematical Programming Models