Inbreeding Properties of Geometric Crossover and Non-geometric Recombinations

Geometric crossover is a representation-independent generalization of traditional crossover for binary strings. It is defined using the distance associated to the search space in a simple geometric way. Many interesting recombination operators for the most frequently used representations are geometric crossovers under some suitable distance. Being a geometric crossover is useful because there is a growing number of theoretical results that apply to this class of operators. To show that a given recombination operator is a geometric crossover, it is sufficient to find a distance for which offspring are in the metric segment between parents associated with this distance. However, proving that a recombination operator is not a geometric crossover requires to prove that such an operator is not a geometric crossover under any distance. In this paper we develop some theoretical tools to prove non-geometricity results and show that some well-known operators are not geometric.

• Type: Conference
• Year: 2007
• Where: FOGA
• Authors: Alberto Moraglio, Riccardo Poli
• Keywords: Artificial Intelligence, FOGA 2007, Geometric Crossover, Recombination Operator, Simple Geometric Way