A New Operator for Efficient Evolutionary Solutions to the Travelling Salesman Problem

In this paper we present two sets of empirical data evaluating the performance of a new Cleanup operator for evolutionary approaches to the travelling salesman problem (TSP). For raw data we have used standard road mileage charts of the USA, Great Britain and Ireland, which enable us to generate a reference table with appropriate city to city distances. A wide variety of standard genetic parameters (population size, epochs, mutation rate and selection type) is explored, and results allow the comparison of performance both with and without our cleanup operator. The cleanup operator improves the convergence speed by reducing the number of epochs required to identify a near-optimal tour; in each instance a significant reduction is convergence time was observed. Our empirical observations show that assisting the evolutionary operators through the use of cleanup gives better performance on this evolutionary encoding. The implication of these findings run contrary to the apparent consensus towards a reduction in the number of genetic operators required [1] by a genetic system for the TSP [2,3]. In these works Fogel concluded that mutation alone was sufficient for this encoding of the TSP problem, rejecting the crossover operator because of its tendency to introduce invalid tours into the population. We have shown that by using the cleanup operator in conjunction with crossover we can effect a more efficient search than a solely mutation-driven approach.