Building Heuristics and Ensembles for the Travel Salesman Problem

Résumé

The Travel Salesman Problem (TSP) is one of the most studied optimization problems due to its high difficulty and its practical interest. In some real-life applications of this problem the solution methods must be very efficient to deal with dynamic environments or large problem instances. For this reasons, low time consuming heuristics as priority rules are often used. Even though such a single heuristic may be good to solve many instances, it may not be robust enough to take the best decisions in all situations so, we hypothesise that an ensemble of heuristics could be much better than the best of those heuristic. We view an ensemble as a set of heuristics that collaboratively build a single solution by combining the decisions of each individual heuristic. In this paper, we study the application of single heuristics and ensembles to the TSP. The individual heuristics are evolved by Genetic Programming (GP) and then Genetic Algorithms (GA) are used to build ensembles from a pool of single heuristics. We conducted an experimental study on a set of instances taken from the TSPLIB. The results of this study provided interesting insights about the behaviour of rules and ensembles.