On Randomness and Structure in Euclidean TSP Instances: A Study With Heuristic Methods

Prediction of the quality of the result provided by a specific solving method is an important factor when choosing how to solve a given problem. The more accurate the prediction, the more appropriate the decision on what to choose when several solving applications are available. In this article, we study the impact of the structure of a Traveling Salesman Problem instance on the quality of the solution when using two representative heuristics: the population-based Ant Colony Optimization (ACO) and the local search Lin-Kernighan (LK) algorithm. The quality of the result for a solving method is measured by the computation accuracy, which is expressed using the percent error between its solution and the optimum one. We classify the instances in structured, semi-structured, and unstructured and perform a between classes and inside-classes analysis. All the structured instances were solved to optimality by the ACO implementation, which was not the case for the LK application. On small random instances, the ACO implementation used in this paper also optimally found the solutions. We show that the quality of the results on semi-structured and unstructured instances can be predicted using some instance parameters when using the ACO implementation. Using the same parameters, the accuracy of the solutions provided by the Lin-Kernighan application cannot be predicted. We also propose several new structured, clustered, and unstructured 2D Euclidean Traveling Salesman Problem instances that can be used by the research community for further investigations.