Abstract
Geometric crossovers are a class of representation-independent search operators for evolutionary algorithms that are well-defined once a notion of distance over a solution space is defined. In this paper we explore the specialisation of geometric crossovers to the permutation representation analysing the consequences of the availability of more than one notion of distance. Also, we study the relations among distances and build a rational picture in which pre-existing recombination operators for permutations fit naturally. Lastly, we illustrate the application of geometric crossover to the Travelling Salesman Problem (TSP).