Crossover Topologico per Permutazioni Topological Crossover for the Permutation Representation

Evolutionary Algorithms (EAs) are successful and widespread general problem solving methods that mimic in a simplified manner biological evolution. Whereas all EAs share the same basic algorithmic structure, they differ in the solution representation – the genotype – and in the search operators employed – mutation and crossover – that are representation-specific. Is this difference only superficial? Is there a deeper unity encompassing all mutation and crossover operators beyond the specific representation, hence all EAs? Topological crossover and topological mutation are representation-independent operators that are well-defined once a notion of distance over the solution space is defined. These operators generalise traditional crossover and mutation operators for binary strings and real vectors. In this paper we explore how the topological framework applies to the permutation representation and in particular analyse the consequences of having more than one notion of distance available. Also, we study the interactions among distances and build a rational picture in which pre-existing recombination/crossover operators for permutation fit naturally. Lastly, we also analyse the application of topological crossover to TSP.