Introduction
The Travelling Salesman Problem (TSP) is one of the classical discrete (combinatorial) optimization problems, encountered in Operations Research (Lawler et al (1985), Clifford & Siu (1995)). TSP is also one of such problems considered as puzzles by mathematicians. Suppose a salesman has to visit n cities (or nodes) cyclically and in one tour he has to visit each city just once, and finish up where he started. In what order should he visit them to minimize the cost or distance or time travelled? Much of the work on the TSP is not motivated by direct applications, but rather by the fact that the TSP provides an ideal platform for the study of general methods that can be applied to a wide range of discrete optimization problems (Grötschel & Holland (1991), Reinelt (1994), Applegate et al (1998), Cook (web document), Hoffman (web document)).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Applegate, R.E. Bixby, V. Chvatal & W. Cook (1998), On the solution of traveling salesman problems, Documenta Mathematica - Extra Volume, ICM –III: 645-658.
S.T. Clifford & W.C. Siu (1995), New approach for solving the travelling salesman problem using self-organizing learning, in: Proc. of the IEEE International Conference on Neural Networks, 5: 2632–2635.
William J. Cook (web document), The Traveling Salesman Problem, (Available online: http://www.tsp.gatech.edu//apps/index.html).
M. Grötschel & O. Holland (1991), Solution of Large Scale Symmetric Traveling Salesman Problems, Mathematical Programming 51: 141-202.
Karla Hoffman (web document), Traveling Salesman Problem, (Available online: http://iris.gmu.edu/~khoffman/papers/trav_salesman.html).
S. Kundu (1997), Min-transitivity of fuzzy leftness relationship and its application to decision making, Fuzzy Sets and Systems 86 (3): 357–367.
E.L. Lawler, JK. Lenstra, A.H.G. Rinnooy Kan & D.B. Shmoys (1985), The Traveling Salesman Problem, Wiley, New York.
G. Reinelt (1994), The Traveling Salesman: Computational Solutions for TSP Applica-tions, Springer-Verlag, Berlin.
Y.M. Wang, J.B. Yang & D.L. Xu (2005), A preference aggregation method through the estimation of utility intervals Computers & Operations Research 32: 2027–2049.
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sengupta, A., Pal, T.K. (2009). Travelling Salesman Problem with Interval Cost Constraints. In: Fuzzy Preference Ordering of Interval Numbers in Decision Problems. Studies in Fuzziness and Soft Computing, vol 238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89915-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-89915-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89914-3
Online ISBN: 978-3-540-89915-0
eBook Packages: EngineeringEngineering (R0)