Dramatically faster Partition Crossover for the traveling salesman problem

Abstract

The Partition Crossover is a deterministic crossover operator for the Traveling Salesman Problem (TSP). It decomposes the union graph of two TSP solutions, A and B, into connected components known as AB-cycles, from which the lower-cost edges are selected and recombined to produce offspring. The operator finds the best offspring within a search space of 2k solutions in linear time, where k is the number of recombining components. We introduce Generalized Partition Crossover 3 (GPX3), a new implementation of Partition Crossover. GPX3 features a new algorithm to quickly find AB-cycles in the union graph. It also identifies additional recombining AB-cycles, expanding the reachable search space. We show that GPX3 runs in O(n) time and is more efficient and effective than previous implementations of Partition Crossover for the TSP.