A New Method for Identification of Recombining Components in the Generalized Partition Crossover

Abstract

Partition crossover operators use information about the interaction between decision variables to recombine solutions. The Generalized Partition Crossover 2 (GPX2) was recently proposed for the Traveling Salesman Problem (TSP). Unlike former partition crossover operators, GPX2 is capable of finding crossover points by splitting vertices of degree 4. GPX2 also finds recombining components with more than two crossover points. The first step of GPX2 is to define candidate components for recombination by finding connected components in the union graph formed by two parents. Some of the candidate components are infeasible for recombination. A candidate component is feasible, i.e., is a recombining component, when the respective (simplified) inner graphs for both parents are equal. We propose a new way of finding recombining components. A recombining component is also identified when there are no mirrored edges between the inner graph of one parent and the outer graph of the other parent. Experiments show that the proposed method generates much more recombination opportunities compared to the original method used in the original GPX2.