A self-organizing neural network using ideas from the immune system to solve the traveling salesman problem

Information Sciences

Volumn 179, Issue 10, 2009, Pages 1454-1468

  Masutti, Thiago A S ^a   de Castro, Leandro N ^b  

^a CATHOLIC UNIVERSITY OF SANTOS   (Brazil)

^b MACKENZIE PRESBYTERIAN UNIVERSITY   (Brazil)

Author keywords

Artificial immune systems; Artificial neural networks; Combinatorial optimization; Self organizing networks; Traveling salesman problem

Indexed keywords

BACKPROPAGATION; COMBINATORIAL OPTIMIZATION; CONVERGENCE OF NUMERICAL METHODS; HEURISTIC METHODS; IMMUNOLOGY; PROBLEM SOLVING; TRAVELING SALESMAN PROBLEM;

ARTIFICIAL IMMUNE SYSTEMS; ARTIFICIAL NEURAL NETWORKS; COMBINATORIAL OP-TIMIZATION PROBLEMS; COMBINATORIAL PROBLEMS; EXHAUSTIVE SEARCHES; IMMUNE SYSTEMS; MODIFIED ALGORITHMS; NP-COMPLETE; NP-HARD CLASS; OPTIMAL SOLUTIONS; PROCESSING TIME; RUNNING TIME; SELF-OR-GANIZING NEURAL NETWORKS; SELF-ORGANIZING NETWORKS;

NEURAL NETWORKS;

EID: 61749097897     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.12.016     Document Type: Article

References (42)

1. Angeniol B., Croix Vaubois G., and Le Texier J.-Y. Self-organizing feature maps and the travelling salesman problem. Neural Networks 1 (1988) 289-293
2. Applegate D., Bixby R., Chvatal V., and Cook W. The Traveling Salesman Problem: A Computational Study (2007), Princeton University Press
3. Aras N., Oommen B.J., and Altinel I.K. The Kohonen network incorporating explicit statistics and its application to the travelling salesman problem. Neural Networks 12 (1999) 1273-1284
4. Bronson R., and Naadimuthu G. Schaum's Outline of Theory and Problems of Operations Research. second ed. (1997), McGraw-Hill
5. Burke L. "Conscientious" neural nets for tour construction in the traveling salesman problem: the vigilant net. Computers and Operations Research 23 (1996) 121-129
6. Burke L.I. Neural methods for the traveling salesman problem: insights from operations research. Neural Networks 7 (1994) 681-690
7. Burke L.I., and Damany P. The guilty net for the traveling salesman problem. Computers and Operations Research 19 (1992) 255-265
8. Cochrane E.M., and Beasley J.E. The co-adaptive neural network approach to the Euclidean travelling salesman problem. Neural Networks 16 (2003) 1499-1525
9. Dantzig G., Fulkerson R., and Johnson S. Solution of a large-scale traveling salesman problem. Operations Research 2 (1954) 393-410
10. de Castro L.N., and Timmis J.I. Artificial Immune Systems: A New Computational Intelligence Approach (2002), Springer-Verlag
11. de Castro L.N. Fundamentals of natural computing: an overview. Physics of Life Reviews 4 (2007) 1-36
12. Durbin R., and Willshaw D. An analogue approach to the travelling salesman problem using an elastic net method. Nature 326 (1987) 689-691
13. Ellabib I., Calamai P., and Basir O. Exchange strategies for multiple ant colony system. Information Sciences 177 (2007) 1248-1264
14. Favata F., and Walker R. A study of the application of Kohonen-type neural networks to the travelling salesman problem. Biological Cybernetics 64 (1991) 463-468
15. Fort J.C. Solving a combinatorial problem via self-organizing process: an application of the Kohonen algorithm to the traveling salesman problem. Biological Cybernetics 59 (1988) 33-40
16. B. Fritzke, P. Wilke, FLEXMAP - a neural network for the traveling salesman problem with linear time and space complexity, in: Proceedings of the International Joint Conference on Neural Networks, IJCNN'91, 1991, pp. 929-934.
17. Garey M.R., and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness (1979), WH Freeman & Co., New York, NY
18. In: Glover F.W., and Kochenberger G.A. (Eds). Handbook of Metaheuristics. International Series in Operations Research and Management Science (2003), Springer
19. Haykin S. Neural Networks: A Comprehensive Foundation. second ed. (1998), Prentice Hall, Upper Saddle River, NJ
20. Helsgaun K. An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operational Research 126 (2000) 106-130
21. S.-J. Kim, J.-H. Kim, H.-M. Choi, An efficient algorithm for traveling salesman problems based on self-organizing feature maps, in: Proceedings of the Second IEEE International Conference on Fuzzy Systems, 1993, pp. 1085-1090.
22. Kirkpatrick S., Gelatt Jr. C.D., and Vecchi M.P. Optimization by simulated annealing. Science 220 (1983) 671-680
23. Kohonen T. Self-Organizing Maps. third ed. (2001), Springer, Berlin
24. In: Lawler E.L., Lenstra J.K., Rinnooy Kan A.H.G., and Shmoys D.B. (Eds). The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (1985), John Wiley & Sons, Chichester
25. Lewis H.R., and Papadimitriou C.H. Elements of the Theory of Computation. second ed. (1997), Prentice-Hall, Upper Saddle River, NJ
26. Lin S., and Kernighan B.W. An effective heuristic algorithm for the traveling-salesman problem. Operations Research 21 (1973) 498-516
27. Looi C.-K. Neural network methods in combinatorial optimization. Computers and Operations Research 19 (1992) 191-208
28. Louis S.J., and Li G. Case injected genetic algorithms for traveling salesman problems. Information Sciences 122 (2000) 201-225
29. T.A.S. Masutti, L.N. de Castro, Uma Abordagem Neuro-Imune para a Solução do Problema de Múltiplos Caixeiros Viajantes (in Portuguese), in: Proceedings of the VIII Brazilian Conference on Neural Networks, Florianópolis, SC, 2007, (CD-ROM).
30. Matsuyama Y. Self-organizing neural networks and various Euclidean traveling salesman problems. Systems and Computers in Japan 23 (1992) 101-112
31. Mérida-Casermeiro E., Galán-Mari{dotless}́n G., and Muñoz-Pérez J. An efficient multivalued Hopfield network for the traveling salesman problem. Neural Processing Letters 14 (2001) 203-216
32. Michalewicz Z., and Fogel D.B. How to Solve It: Modern Heuristics (2000), Springer-Verlag, New York, NY
33. Padberg M., and Rinaldi G. A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Review 33 (1991) 60-100
34. R. Pasti, L.N. de Castro, A Neuro-immune network for solving the traveling salesman problem, in: Proceedings of International Joint Conference on Neural Networks, IJCNN'06, 2006, pp. 3760-3766.
35. Rardin R.L. Optimization in Operations Research (1997), Prentice-Hall, Upper Saddle River, NJ
36. Reilly R., and Tchimev P. Neural network approach to solving the traveling salesman problem. Journal of Computing Sciences in Colleges 19 (2003) 41-61
37. Reinelt G. TSPLIB - a traveling salesman problem library. ORSA Journal on Computing 3 (1991) 376-384
38. Smith K.A., Palaniswami M., and Krishnamoorthy M. Neural techniques for combinatorial optimization with applications. IEEE Transactions on Neural Networks 9 (1998) 1301-1318
39. Smith K. Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS Journal on Computing 11 (1999) 15-34
40. Somhom S., Modares A., and Enkawa T. A self-organising model for the travelling salesman problem. Journal of the Operational Research Society 48 (1997) 919-928
41. Somhom S., Modares A., and Enkawa T. Competition-based neural network for the multiple travelling salesmen problem with minmax objective. Computers and Operations Research 26 (1999) 395-407
42. Wang L. On the dynamics of discrete-time, continuous-state Hopfield neural networks. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 45 (1998) 747-749