Evolving ensembles of heuristics for the travelling salesman problem

Abstract

Abstract The Travelling Salesman Problem (TSP) is a well-known optimisation problem that has been widely studied over the last century. As a result, a variety of exact and approximate algorithms have been proposed in the literature. When it comes to solving large instances in real-time, greedy algorithms guided by priority rules represent the most common approach, being the nearest neighbour (NN) heuristic one of the most popular rules. NN is quite general but it is too simple and so it may not be the best choice in some cases. Alternatively, we may design more sophisticated heuristics considering the particular features of families of instances. To do that, we have to consider problem attributes other than the proximity of the next city to build priority rules. However, this process may not be easy for humans and so it is often addressed by some learning procedure. In this regard, hyper-heuristics as Genetic Programming (GP) stands as one of the most popular approaches. Furthermore, a single heuristic, even being good in average, may not be good for a number of instances of a given set. For this reason, the use of ensembles of heuristics is often a good alternative, which raises the problem of building ensembles from a given set of heuristic rules. In this paper, we study the application of two kinds of ensembles to the TSP. Given a set of TSP instances having similar characteristics, we firstly exploit a GP to build a set of heuristics involving a number of problem attributes, and then we build ensembles combining these heuristics by means of a Genetic Algorithm (GA). The experimental study provided valuable insights into the construction and utilisation of single rules and ensembles. It clearly demonstrated that the performance of ensembles justifies the time invested when compared to using individual heuristics.