Transformations of generalized ATSP into ATSP

Operations Research Letters

Volumn 31, Issue 5, 2003, Pages 357-365

  Ben Arieh, D ^a   Gutin, G ^b   Penn, M ^c   Yeo, A ^b   Zverovitch, A ^b  

^a Sunflower Networking Group   (United States)

^b UNIVERSITY OF LONDON   (United Kingdom)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Domination analysis; Generalized TSP; Heuristics; TSP

Indexed keywords

ALGORITHMS; GRAPH THEORY; HEURISTIC METHODS; SET THEORY; TRAVELING SALESMAN PROBLEM;

DOMINATION ANALYSIS;

OPERATIONS RESEARCH;

EID: 0038825569     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(03)00031-2     Document Type: Article

References (25)

1. D. Applegate, R.E. Bixby, V. Chvátal, W. Cook, On the solution of traveling salesman problems, Doc. Math., J. DMV, Extra Vol. ICM Berlin 1998, III (1998) 645-656. The Concorde code is currently available from http://www.math.princeton.edu/tsp/concorde.html.
2. D. Ben-Arieh, G. Gutin, M. Penn, A. Yeo, A. Zverovitch, Process planning for rotational parts and the generalized traveling salesman problem. Int. J. Prod. Res., to appear.
3. Dimitrijević V., Sarić Z. An efficient transformation of the generalized traveling salesman problem into the traveling salesman problem on digraphs. Inf. Sci. 102:1997;105-110.
4. Fischetti M., Salazar J.J., Toth P. The symmetric generalized traveling salesman polytope. Networks. 26:1995;113-123.
5. Fischetti M., Salazar J.J., Toth P. A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Oper. Res. 45:1997;378-394.
6. Fischetti M., Salazar J.J., Toth P. Exact methods for the ATSP. Gutin G., Punnen A.P. Traveling Salesman Problem and its Variations. 2002;Kluwer Academic Publishers, Dordrecht.
7. Fischetti M., Salazar J.J., Toth P. The generalized traveling salesman and orienteering problem. Gutin G., Punnen A.P. Traveling Salesman Problem and its Variations. 2002;Kluwer Academic Publishrers, Dordrecht.
8. Glover F., Gutin G., Yeo A., Zverovich A. Construction heuristics for the asymmetric TSP. Eur. J. Oper. Res. 129:2001;555-568.
9. Glover F., Punnen A.P. The travelling salesman problem: new solvable cases and linkages with the development of approximation algorithms. J. Oper. Res. Soc. 48:1997;502-510.
10. G. Gutin, A.P. Punnen (Eds.), Traveling Salesman Problem and its Variations, Kluwer Academic Publishrers, Dordrecht, 2002.
11. Gutin G., Yeo A., Zverovitch A. Exponential Neighborhoods and Domination Analysis for the TSP. Gutin G., Punnen A.P. Traveling Salesman Problem and its Variations. 2002;Kluwer Academic Publishrers, Dordrecht.
12. Laporte G., Asef-Vaziri A., Sriskandarajah C. Some applications of the generalized traveling salesman problem. J. Oper. Res. Soc. 47:1996;1461-1467.
13. Laporte G., Mercure H., Nobert Y. Generalized travelling salesman problem through. n sets of nodes the asymmetrical cases Discrete Appl. Math. 18:1987;185-197.
14. Laporte G., Nobert Y. Generalized travelling salesman through. n sets of nodes an integer programming approach INFOR. 21:1983;61-75.
15. Laporte G., Semet F. Computational evaluation of a transformation procedure for the symmetric generalized traveling salesman problem. INFOR. 37:1999;114-120.
16. E.L. Lawler, J.K. Lenstra, A.H.G. Rinooy Kan, D.B. Shmoys (Eds.), Travelling Salesman Problem: a Guided Tour of Combinatorial Optimization, Wiley, Chichester, 1985.
17. Lien Y., Ma E., Wah B.W.S. Transformation of the generalized traveling salesman problem into the standard traveling salesman problem. Information Sci. 74:1993;177-189.
18. C.E. Noon, The generalized traveling salesman problem, Ph.D. Thesis, Department of Industrial and Operations Research, University of Tennessee, 1988.
19. Noon C.E., Bean J.C. A Lagrangian based approach for the asymmetric generalized traveling salesman problem. Oper. Res. 39:1991;623-632.
20. Noon C.E., Bean J.C. An efficient transformation of the generalized traveling salesman problem. INFOR. 31:1993;39-44.
21. Punnen A.P., Kabadi S. Domination analysis of some heuristics for the traveling salesman problem. Discrete Appl. Math. 119:2002;117-128.
22. Punnen A.P., Margot F., Kabadi S. TSP heuristics: domination analysis and complexity. Algorithmica. 35:2003;111-127.
23. Reinelt G. TSPLIB - A traveling salesman problem library. ORSA J. Comput. 3:1991;376-384. http://www.crpc.rice.edu/softlib/tsplib/ .
24. J.J. Salazar, Algoritmi per il problema del commesso viaggiatore generalizzato, Ph.D. Thesis, Royal Spanish College in Bologna, 1992 (in Italian).
25. M.M. Sepehri, The symmetric generalized travelling salesman problem, Ph.D. Thesis, University of Tennessee, Knoxville, 1991.