A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem

Authors:
Olaf Mersmann;Bernd Bischl;Heike Trautmann;Markus Wagner;Jakob Bossek;Frank Neumann
Affiliations:
Statistics Faculty, TU Dortmund University, Dortmund, Germany 44221;Statistics Faculty, TU Dortmund University, Dortmund, Germany 44221;Statistics Faculty, TU Dortmund University, Dortmund, Germany 44221;School of Computer Science, The University of Adelaide, Adelaide, Australia 5005;Statistics Faculty, TU Dortmund University, Dortmund, Germany 44221;School of Computer Science, The University of Adelaide, Adelaide, Australia 5005
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2013

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Abstract

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesperson 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.