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An Analysis of Several Heuristics for the Traveling Salesman Problem

Daniel J. Rosenkrantz, Richard E. Stearns, Philip M. Lewis, II
1977 SIAM journal on computing (Print)  
Several polynomial time algorithms finding "good," but not necessarily optimal, tours for the traveling salesman problem are considered.  ...  It is also shown that for any n ≥ 8, there are traveling salesman problems with n nodes having tours which cannot be improved by making n/4 edge changes, but for which the ratio is 2(1 − 1/n).  ...  Introduction The traveling salesman problem has long been of great interest. The problem has been formulated in several different ways.  ... 
doi:10.1137/0206041 fatcat:qboogsamejbwheikcy5bxupatq

An analysis of several heuristics for the traveling salesman problem [chapter]

Daniel J. Rosenkrantz, Richard E. Stearns, Philip M. Lewis
2009 Fundamental Problems in Computing  
Several polynomial time algorithms finding "good," but not necessarily optimal, tours for the traveling salesman problem are considered.  ...  It is also shown that for any n ≥ 8, there are traveling salesman problems with n nodes having tours which cannot be improved by making n/4 edge changes, but for which the ratio is 2(1 − 1/n).  ...  Introduction The traveling salesman problem has long been of great interest. The problem has been formulated in several different ways.  ... 
doi:10.1007/978-1-4020-9688-4_3 dblp:conf/birthday/RosenkrantzSL13 fatcat:soysg73oprdvjmdvneahkjezpa

Page 452 of The Journal of the Operational Research Society Vol. 56, Issue 4 [page]

2005 The Journal of the Operational Research Society  
An analysis of several heuristics for the traveling salesman problem. SJAM J Comput 6: 563-581. Received March 2003; accepted May 2004 after two revisions  ...  An empirical study of a new metaheuristic for the traveling salesman problem. Eur J Opl Res 104: 113-128 Or I (1976).  ... 

Page 136 of Journal of Research and Practice in Information Technology Vol. 12, Issue 4 [page]

1980 Journal of Research and Practice in Information Technology  
ROSENKRANTZ, D.j., STEARNS, R.E., and LEWIS, R.M., An Analysis of Several Heuristics for the Travelling Salesman Problem, S/AM Journal on Computing, Vol. 6, No. 3, 1977, pp. 563-581. 26.  ...  ., An Effective Heuristic Algorithm for the Travelling Salesman Problem, Operations Research, 21, 1973, pp. 498-516. 22.  ... 

Page 426 of The Journal of the Operational Research Society Vol. 46, Issue 4 [page]

1995 The Journal of the Operational Research Society  
Lewis (1977) An analysis of several heuristics for the traveling salesman problem. SIAM J. Comp. 6, 563-581. S. Lin (1965) Computer solutions of the traveling salesman problem. Bell Syst. Tech.  ...  E1ton (1972) Algorithms for large-scale traveling salesman problems. Op/ Res. Q. 23, 511-518. S. Lin and B. KERNIGHAN (1973) An effective heuristic algorithm for the traveling salesman problem.  ... 

Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics [chapter]

Stefan Klootwijk, Bodo Manthey, Sander K. Visser
2018 Lecture Notes in Computer Science  
Using this, we conduct a probabilistic analysis of some simple heuristics on these random shortest path metrics.  ...  of the vertices.  ...  Theorem 3 Any insertion heuristic heuristic for the traveling salesman problem has an expected approximation ratio of O(β/α) on generalized random shortest path metrics.  ... 
doi:10.1007/978-3-030-10564-8_9 fatcat:7l4boyd2kzdjhpphil3fkfmmme

Exact time-efficient combined algorithm for solving the asymmetric traveling salesman problem

Galina Zhukova, Mikhail Ulyanov, Mikhail Fomichev
2018 Business Informatics  
Quite often, the features of these problems lead to the traveling salesman problem in asymmetric formulation (asymmetric traveling salesman problem, ATSP).  ...  Аbstract For practical, important tasks in the fi elds of economics and logistics, as well as in a number of technical applications, it becomes necessary to solve the traveling salesman problem (TSP).  ...  The authors see the further development of the study in a more detailed analysis of the distributions of running time of software implementations of the algorithms.  ... 
doi:10.17323/1998-0663.2018.3.20.28 fatcat:t3rmmrc3mjdy3mhyghz6chly2u

On the Significance of the Initial Solution in Travelling Salesman Heuristics

Jukka Perttunen
1994 Journal of the Operational Research Society  
KerniGHAN (1973) An effective heuristic algorithm for the traveling salesman problem. Opns Res. 21, 498-516. . A. Aprasinski and M. M.  ...  Computational experiments are carried out for several commonly applied edge exchange heuristics and randomly generated Euclidean travelling salesman problems.  ... 
doi:10.1038/sj/jors/0451004 fatcat:s6pfupewqfamzf4csavf27nwi4

On the Significance of the Initial Solution in Travelling Salesman Heuristics

Jukka Perttunen
1994 Journal of the Operational Research Society  
KerniGHAN (1973) An effective heuristic algorithm for the traveling salesman problem. Opns Res. 21, 498-516. . A. Aprasinski and M. M.  ...  Computational experiments are carried out for several commonly applied edge exchange heuristics and randomly generated Euclidean travelling salesman problems.  ... 
doi:10.1057/jors.1994.183 fatcat:ijey66m5vbbztgayupvv7peoxe

A Review of the Optimization Algorithms on Traveling Salesman Problem

N. Sathya, A. Muthukumaravel
2015 Indian Journal of Science and Technology  
optimal solution for the traveling salesman problem.  ...  It also relates the traveling salesman problem with the available algorithms and provides the advantages in providing a solution for TSP.  ...  Not much research was encountered in the survey over problem space analysis of the Traveling Salesman problem.  ... 
doi:10.17485/ijst/2015/v8i1/84652 fatcat:pigy2l32bzh7nnjcqmmnqa354u

The Stochastic Capacitated Traveling Salesmen Location Problem: A Computational Comparison for a United States Instance

Luca Bertazzi, Francesca Maggioni
2014 Procedia - Social and Behavioral Sciences  
For this problem, we compare the performance of two different approaches.  ...  The first is a solution based on a heuristic proposed for a similar well known problem and the second is a solution based on a stochastic second-order cone model.  ...  We compare the performance of two different approaches: the first one based on the heuristic proposed by Simchi-Levi (1991) and the second one as a two-stage stochastic second-order cone programming  ... 
doi:10.1016/j.sbspro.2013.12.819 fatcat:2rd53ca5ufgx7gnmjolmhjimli

The Solution of Travelling Salesman Problems Based on Industrial Data

Buddhadev Roychoudhury, John F. Muth
1995 Journal of the Operational Research Society  
Hirt (1982) An experimental comparison of human schedulers and heuristic algorithms for the traveling salesman problem. J. Opns Mgmt 2, 215-223. 4. R. L. Kara and G. L.  ...  KERNiIGHAN (1973) An effective heuristic algorithm for the travelling salesman problem. Opns Res. 21, 498-516. . F. R. Jacoss, K. Matuieson, J. F. Mutu and T. M.  ... 
doi:10.1057/jors.1995.49 fatcat:umkqtgrknnathasedttdq2gceq

Combinatorial optimization and vehicle fleet planning: Perspectives and prospects

T. L. Magnanti
1981 Networks  
ACKNOWLEDGEMENTS I am grateful to Bruce Golden, Steve Graves, Jan Hammond, and Paul Mireault for their comments on an earlier version of this paper.  ...  ., per- formance guarantee) analysis ([20], [109]), statistical analysis ([56]), and probabilistic analysis ([71], [72]) of various heuristics for the traveling salesman problem typified this period  ...  For this problem, for any fixed values of the demand point to vehicle assignment variables Yiv' the model decomposes into a traveling salesman problem for each vehicle and an inventory allocation problem  ... 
doi:10.1002/net.3230110209 fatcat:kmmvt63wbjcppep5ak6zvhc7em

Page 5107 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
solution of traveling salesman problems.  ...  By using this idea we show that for a class of distance matrices an optimal tour of the traveling salesman problem can be computed in polynomial time.”  ... 

Page 5719 of Mathematical Reviews Vol. , Issue 85m [page]

1985 Mathematical Reviews  
Author’s summary: “In this paper we analyze the probabilistic performance of some heuristics for the travelling salesman prob- lem (TSP) and the maximum weight travelling salesman problem (MWTSP).  ...  For larger examples, the solution of the heuristic is compared to several bounds. An efficient method for performing sensitivity analysis is also indicated.” Marbukh, V.  ... 
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