Evaluation of Traveling Salesman Problem Instance Hardness by Clustering.

Traveling salesman problem (TSP) is a well-known NP-hard combinatorial optimization problem. It has been solved by a number of exact and approximate algorithms and serves as a testbed for new heuristic and metaheuristic optimization algorithms. However, it is often not easy to evaluate the hardness (complexity) of a TSP instance. Simple measures such as the number of cities or the minimum (maximum) route length do not capture the internal structure of a TSP instance sufficiently. In this work, we propose a new method for the assessment of TSP instance complexity based on clustering. The new approach is evaluated on a set of randomized TSP instances with different structure and its relation to the performance of a selected metaheuristic TSP solver is studied.