A parallel ensemble genetic algorithm for the traveling salesman problem

Abstract

A parallel ensemble of Genetic Algorithms for the Traveling Salesman Problem (TSP) is proposed. Different TSP solvers perform efficiently on different instance types. However, finding the best solver for all instances is challenging. A hybrid of the Mixing Genetic Algorithm (MGA) and Edge Assembly Crossover (EAX) has been shown to perform well on hard instances. The MGA uses Generalized Partition Crossover (GPX) to find the best and worst out of 2k possible solutions, where k is a decomposition factor of two-parent tours. MGA mixes the edges without any loss of diversity in the population. The best individuals move to the top of the population. The worst individuals are filtered to the bottom of the population. Previously, MGA was applied to TSP instances with less than 4,500 vertices. In this article, various Island Model implementations of MGA are introduced to handle larger problem sizes. The island model uses two mixing policies - migration, which does not lose diversity, and replacement, which loses some population diversity. The islands are configured in two patterns - a ring and a hypercube. An ensemble running multiple versions of an hybrid of MGA and EAX algorithms yields excellent performance for problems as large as 85,900.