Local search and the traveling salesman problem: a feature-based characterization of problem hardness

Authors:
Olaf Mersmann;Bernd Bischl;Jakob Bossek;Heike Trautmann;Markus Wagner;Frank Neumann
Affiliations:
Statistics Faculty, TU Dortmund University, Germany;Statistics Faculty, TU Dortmund University, Germany;Statistics Faculty, TU Dortmund University, Germany;Statistics Faculty, TU Dortmund University, Germany;School of Computer Science, The University of Adelaide, Australia;School of Computer Science, The University of Adelaide, Australia
Venue:
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Year:
2012

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Abstract

With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.