TY - JOUR
T1 - On the asymptotic behavior of subtour-patching heuristics in solving the TSP on permuted Monge matrices
AU - Deǐneko, Vladimir G.
AU - Shabtay, Dvir
AU - Steiner, George
N1 - Funding Information:
Acknowledgements The authors thank two anonymous referees for their comments, which led to an improved presentation for the paper. This research was partially supported by the Centre for Discrete Mathematics and Its Applications, University of Warwick and by the United Kingdom EPRSC fund EP/F017871, and by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev. Partial support by the Natural Sciences and Engineering Research Council of Canada under Grant No. 041798 is also gratefully acknowledged.
PY - 2011/2/1
Y1 - 2011/2/1
N2 - We examine the performance of different subtour-patching heuristics for solving the strongly NP-hard traveling salesman problem (TSP) on permuted Monge matrices. We prove that a well-known heuristic is asymptotically optimal for the TSP on product matrices and k-root cost matrices. We also show that the heuristic is provably asymptotically optimal for general permuted Monge matrices under some mild conditions. Our theoretical results are strongly supported by the findings of a large-scale experimental study on randomly generated numerical examples, which show that the heuristic is not only asymptotically optimal, but also finds optimal TSP tours with high probability that increases with the problem size. Thus the heuristic represents a practical tool to solve large instances of the problem.
AB - We examine the performance of different subtour-patching heuristics for solving the strongly NP-hard traveling salesman problem (TSP) on permuted Monge matrices. We prove that a well-known heuristic is asymptotically optimal for the TSP on product matrices and k-root cost matrices. We also show that the heuristic is provably asymptotically optimal for general permuted Monge matrices under some mild conditions. Our theoretical results are strongly supported by the findings of a large-scale experimental study on randomly generated numerical examples, which show that the heuristic is not only asymptotically optimal, but also finds optimal TSP tours with high probability that increases with the problem size. Thus the heuristic represents a practical tool to solve large instances of the problem.
KW - Asymptotically optimal
KW - Strongly NP-hard
KW - Subtour-patching heuristic
KW - Traveling salesman problem
UR - http://www.scopus.com/inward/record.url?scp=79951554136&partnerID=8YFLogxK
U2 - 10.1007/s10732-010-9127-1
DO - 10.1007/s10732-010-9127-1
M3 - Article
AN - SCOPUS:79951554136
SN - 1381-1231
VL - 17
SP - 61
EP - 96
JO - Journal of Heuristics
JF - Journal of Heuristics
IS - 1
ER -