Identificação de componentes recombinantes no generalized partition crossover

Abstract

The Traveling Salesman Problem (TSP) is one of the best-known optimization problems and consists of finding the shortest Hamiltonian circuit for a set of vertices. Partition Crossover (PX) is an important recombination operator developed for the TSP. It generates offspring by the recombination of connected components found after removing shared edges from the graph formed by the union of parent solutions. The operator then determines which components can be recombined to generate offspring. However, not every connected component can be recombined. To identify recombining components, the operator applies a test comparing the simplified graphs of parent solutions within the component, called inner graphs. An inner graph simplifies one solution paths within a component. If solutions inner graphs are equal, the component is a recombining component. However, one can demonstrate that there are recombining components not identified by the operator. Based on the study of the relation between simplified graphs and perfect matchings, a concept from Graph Theory, this work proposes two additional tests. Experiments show that PX can find more recombining components applying the proposed tests, hence improving operator performance.