Very greedy crossover in a genetic algorithm for the traveling salesman problem

Abstract

In the traveling salesman problem, we are given a set of cities and the distances between them, and we seek a shortest tour that visits each city exactly once and returns to the starting city. Many researchers have described genetic algorithms for this problem, and they have often focused on the crossover operator, which builds offspring tours by combining two parental tours. Very greedy crossover extends several of these operators; as it builds a tour, it always appends the shortest parental edge to a city not yet visited, if there is such an edge. A steady-state genetic algorithm using this operator, mutation by inversion, and rank-based probabilities for both selection and deletion shows good results on a suite of five test problems.