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An Analysis of Several Heuristics for the Traveling Salesman Problem

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. ...

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

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. ...

##
###
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]

2018
*
Lecture Notes in Computer Science
*

Using this, we conduct a probabilistic

doi:10.1007/978-3-030-10564-8_9
fatcat:7l4boyd2kzdjhpphil3fkfmmme
*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. ...##
###
Exact time-efficient combined algorithm for solving the asymmetric traveling salesman problem

2018
*
Business Informatics
*

Quite often,

doi:10.17323/1998-0663.2018.3.20.28
fatcat:t3rmmrc3mjdy3mhyghz6chly2u
*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. ...##
###
On the Significance of the Initial Solution in Travelling Salesman Heuristics

1994
*
Journal of the Operational Research Society
*

KerniGHAN (1973)

doi:10.1038/sj/jors/0451004
fatcat:s6pfupewqfamzf4csavf27nwi4
*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*. ...##
###
On the Significance of the Initial Solution in Travelling Salesman Heuristics

1994
*
Journal of the Operational Research Society
*

KerniGHAN (1973)

doi:10.1057/jors.1994.183
fatcat:ijey66m5vbbztgayupvv7peoxe
*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*. ...##
###
A Review of the Optimization Algorithms on Traveling Salesman Problem

2015
*
Indian Journal of Science and Technology
*

optimal solution

doi:10.17485/ijst/2015/v8i1/84652
fatcat:pigy2l32bzh7nnjcqmmnqa354u
*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*. ...##
###
The Stochastic Capacitated Traveling Salesmen Location Problem: A Computational Comparison for a United States Instance

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 ...

##
###
The Solution of Travelling Salesman Problems Based on Industrial Data

1995
*
Journal of the Operational Research Society
*

Hirt (1982)

doi:10.1057/jors.1995.49
fatcat:umkqtgrknnathasedttdq2gceq
*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. ...##
###
Combinatorial optimization and vehicle fleet planning: Perspectives and prospects

1981
*
Networks
*

ACKNOWLEDGEMENTS I am grateful to Bruce Golden, Steve Graves, Jan Hammond, and Paul Mireault

doi:10.1002/net.3230110209
fatcat:kmmvt63wbjcppep5ak6zvhc7em
*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*...##
###
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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