Genetic algorithm for asymmetric traveling salesman problem with imprecise travel times

Journal of Computational and Applied Mathematics

Volumn 235, Issue 9, 2011, Pages 3063-3078

  Majumdar, J ^a   Bhunia, A K ^b  

^a DURGAPUR GOVERNMENT COLLEGE   (India)

^b UNIVERSITY OF BURDWAN   (India)

Author keywords

Asymmetric traveling salesman problem; Combinatorial optimization; Genetic algorithm; Interval order relation

Indexed keywords

COMBINATORIAL OPTIMIZATION; DECISION MAKING; GENETIC ALGORITHMS; TRAVEL TIME;

ASYMMETRIC TRAVELING SALESMAN PROBLEM; COMPUTATIONAL STUDIES; FITNESS FUNCTIONS; GENETIC OPERATORS; INTERVAL ARITHMETIC; INTERVAL NUMBER; INTERVAL ORDERS; INTERVAL-VALUED;

TRAVELING SALESMAN PROBLEM;

EID: 79951514207     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.12.027     Document Type: Article

References (58)

1. S. Lin, and B.W. Kernighan An effective heuristic algorithm for the traveling salesman problem Oper. Res. 21 1973 498 516
2. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys The Traveling Salesman Problem: G.E. Re Guided Tour of Combinatorial Optimization 1985 Wiley and Sons New York
3. G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson Solution of a large-scale traveling-salesman problem Oper. Res. 2 1954 393 410
4. M. Padberg, and G. Rinaldi Optimization of a 532-city symmetric traveling salesman problem by branch and cut Oper. Res. 6 1987 1 7 (Pubitemid 17601864)
5. W.L. Eastman, Linear programming with pattern constraints, Ph.D. Thesis, Harvard University, Cambridge, MA, 1958.
6. M. Held, and R.M. Karp The traveling salesman problem and minimum spanning trees: part II Math. Program. 1 1971 6 25
7. E. Balas, and N. Christofids A restricted Lagrangian approach to the traveling salesman problem Math. Program. 21 1981 19 46 (Pubitemid 12508253)
8. H. Crowder, and M.W. Padberg Solving large-scale symmetric traveling salesman problems to optimality Manage. Sci. 26 1980 495 509
9. M.W. Padberg, and S. Hong On the symmetric traveling salesman problem: a computational study Math. Prog. Stud. 12 1980 78 107
10. M. Grtschel, and O. Holland Solution of large-scale symmetric traveling salesman problems Math. Program. 51 1991 141 202 (Pubitemid 21708534)
11. B.E. Bellman Dynamic programming treatment of the traveling salesman problem J. Assoc. Comput. Mach. 9 1963
12. . Ergan, and J.B. Orlin A dynamic programming methodology in very large scale neighbourhood search applied to the traveling salesman problem Discrete Optim. 3 2006 78 85 (Pubitemid 43276319)
13. D.S. Johnson More approaches to the traveling salesman guide Nature 330 1987 525
14. G.A. Croes A method for solving traveling salesman problems Oper. Res. 6 1958 791 812
15. O. Martin, S.W. Otto, and E.W. Felten Large step Markov chains for the traveling salesman problem Complex Systems 2 1991 299 326
16. J. Knox, The application of Tabu search to the symmetric traveling salesman problem, Ph.D. Dissertation, University of Colorado, 1989.
17. C.-N. Fiechter, A parallel Tabu search algorithm for large scale traveling salesman problems, Working Paper 90/1, Dpartment de Mathmatiques, cole Polytechnique, Fdrale de Lausanne, 1990.
18. F. Glover Artificial intelligence, heuristic frameworks and Tabu search Manag. Decis. Econom. 11 1990
19. J.J. Hopfield, and D.W. Tank Neural computation of decisions in optimization problems Biol. Cybernet. 52 1985
20. S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi Optimization by simulated annealing Science 220 1983 671 680
21. E. Bonomi, and J.-L. Lutton The N-city traveling salesman problem: statistical mechanics and the metropolis algorithm SIAM Rev. 26 1984 551 568 (Pubitemid 17491613)
22. S. Kirkpatrick, and G. Toulouse Configuration space analysis of traveling salesman problems J. Phys. 46 1985 1277 1292
23. B.L. Golden, and C.C. Skiscim Using simulated annealing to solve routing and location problems Naval Res. Logist. Quart. 33 1986 261 280
24. J. Lam, An efficient simulated annealing schedule, Ph.D. Dissertation, Department of Computer Science, Yale University, 1988.
25. S. Nahar, S. Sahni, and E. Shragowitz Simulated annealing and combinatorial optimization Int. J. Comp. Aided VLSI Des. 1 1989 1 23
26. C.C. Lo, and C.C. Hus An annealing framework with learning memory IEEE Trans. Syst. Man Cybern. A 28 1998 1 13
27. J.J. Grefenstette, R. Gopal, B. Rosimaita, D. Van Gucht, Genetic algorithms for the traveling salesman problem, in: Proceedings of the International Conference on Genetic Algorithms and their Applications, 1985, pp. 160168.
28. H.D. Nguyen, I. Yoshihara, K. Yamamori, and M. Yasunaga Implementation of an effective hybrid GA for large-scale traveling salesman problems IEEE Trans. Syst. Man Cybern. B 37 2007 92 99 (Pubitemid 46358484)
29. D.E. Goldberg Genetic Algorithms in Search, Optimization and Machine Learning 1989 Addison-Wesley New York
30. P. Jog, J.Y. Suh, D. Van Gucht, The effect of population size, heuristic crossover and local improvement on a genetic algorithm for the traveling salesman problem, in: Proceedings of the Third International Conference on Genetic Algorithms and their Applications, 1989, pp. 110115.
31. D. Whitley, T. Starkweather, D'Ann Fuquay, Scheduling problems and traveling salesman: the genetic edge recombination operator, in: Proceedings of the Third International Conference on Genetic Algorithms and their Applications, 1989, pp. 133140.
32. H.C. Braun On solving traveling salesman problems by genetic algorithm H.P. Schwefel, R. Manner, Parallel Problem Solving from Nature Lecture Notes in Computer Science vol. 496 1991 129 133
33. P. Larranaga, C. Kuijpers, R. Murga, I. Inza, and S. Dizdarevic Genetic algorithms for the traveling salesman problem: a review of representations and operators Artif. Intell. Rev. 13 1999 129 170
34. L. Yang, and D.A. Stacey Solving the Traveling Salesman Problem Using the Enhanced Genetic Algorithm 2001 Springer-Verlag pp. 307316
35. S.S. Ray, S. Bandyopadhyay, S.K. Pal, New operators of genetic algorithms for traveling salesman problem, Cambridge, UK, ICPR-04 2, 2004, pp. 497500.
36. R. Baraglia, J.I. Hidalgo, and R. Perego A Parallel Hybrid Heuristic for the TSP 2001 Springer-Verlag pp. 193202
37. P. Gang, I. Iimura, H. Tsurusawa, and S. Nakayama Genetic Local Search Based on Genetic Recombination: A Case for Traveling Salesman Problem 2004 Springer-Verlag pp. 202212
38. H.K. Tsai, J.M. Yang, Y.F. Tsai, and C.Y. Kao Some issues of designing genetic algorithms for traveling salesman problems Soft Comput. 8 2004 689 697 Springer-Verlag
39. S.B. Liu, K.M. Ng, and H.L. Ong A new heuristic algorithm for the classical symmetric traveling salesman problem Int. J. Math. Sci. 1 4 2007 234 238
40. B.F. Al-Dulaimi, H.A. Ali, Enhanced traveling salesman problem solving by genetic algorithm technique (TSPGA), in: Proceedings of World Academy of Science, Engineering and Technology, vol. 28, April 2008, pp. 296302.
41. G. Laporte The traveling salesman problem: an overview of exact and approximate algorithms European J. Oper. Res. 59 1992 231 247 (Pubitemid 23565197)
42. D.S. Johnson, and L.A. McGeoch The traveling salesman problem: a case study E. Aarts, J.K. Lenstra, Loca; Search in Combinatorial Optimization 1997 John Wiley & Sons New York 215 310
43. D.L. Applegate, R.E. Bixby, V. Chvatal, and W.J. Cook The Traveling Salesman Problem: A Computational Study 2006 Princeton University Press Princeton
44. C.H. Papadimitriou, and K. Steiglitz The complexity of local search for the traveling salesman problem SIAM J. Comput. 6 1977 78 83
45. T.H.C. Smith, V. Srinivasan, and G.L. Thompson Computational performance of three subtour elimination algorithms for solving asymmetric traveling salesman problems Ann. Discrete Math. 1 1977 495 506
46. G. Carpaneto, and P. Toth Some new branching and bounding criteria for the asymmetric traveling salesman problem Manage. Sci. 26 1980 736 743
47. J. Cirasella, D.S. Johnson, L.A. McGeoch, and W. Zhang The asymmetric traveling salesman problem: algorithms, instance generators, and tests ALENEX Proceedings Springer Lecture Notes in Computer Science vol. 2153 2001 32 59 (Pubitemid 33340063)
48. E.K. Burke, P.I. Cowling, and R. Keuthen Effective local and guided variable neighbourhood search methods for the asymmetric travelling salesman problem E.J.W. Boers, EvoWorkshop Springer Lecture Notes in Computer Science vol. 2037 2001 203 212 (Pubitemid 33261169)
49. D.S. Johnson, G. Gutin, L.A. McGeoch, A. Yeo, W. Zhang, and A. Zverovitch Experimental analysis of heuristics for the ATSP Gutin Punnen The Traveling Salesman Problem and its Variations 2002 Kluwer Academic Publisher 445 487
50. I.C. Choi, S.I. Kim, and H.S. Kim A genetic algorithm with a mixed region search for the asymmetric traveling salesman problem Comput. Oper. Res. 30 2003 773 786
51. H. Ishibuchi, and H. Tanaka Multiobjective programming in optimization of the interval objective function European J. Oper. Res. 48 1990 219 225
52. S. Chanas, and D. Kuchta Multiobjective programming in optimization of interval objective functionsa generalized approach European J. Oper. Res. 94 1996 594 598 (Pubitemid 126391964)
53. A. Sengupta, and T.K. Pal Theory and methodology on comparing interval numbers European J. Oper. Res. 127 2000 28 43
54. J. Majumdar, and A.K. Bhunia Elitist genetic algorithm for assignment problem with imprecise goal European J. Oper. Res. 177 2007 684 692
55. A. Sengupta, and T.K. Pal Travelling salesman problem with interval cost constraints Fuzzy Preference Ordering of Interval Numbers in Decision Problems 2009 Springer 111 119
56. R. Montemanni, J. Barta, M. Mastrolilli, and L.M. Gambardella The robust traveling salesman problem with interval data Transp. Sci. 41 3 2007 366 381
57. S.K. Mahato, and A.K. Bhunia Interval-arithmetic-oriented interval computing technique for global optimization AMRX Appl. Math. Res. Exp. 2006 2006 1 19
58. Z. Michalewicz Genetic Algorithms + Data Structure = Evolution Programs 1999 Springer-Verlag Berlin