Nothing Special   »   [go: up one dir, main page]

Skip to main content

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 55))

  • 895 Accesses

Abstract

This work describes the application of the MAX-MIN Ant System algorithm to solve the Undirected Rural Postman Problem. The results obtained when we apply the proposed solution to a data set used by other authors demonstrate that this approach is very good. Moreover, the method only requires the graph formulation of the problem, so that no complex mathematical formulation of the same is required.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Deneubourg, J.L., Aron, S., Goss, S., Pasteels, J.M.: The self-organizing exploratory pattern of the argentine ant. J. Insect Behav. 3, 159–168 (1990)

    Article  Google Scholar 

  2. Dorigo, M.: Optimization, learning and natural algorithms. Ph.D. thesis, Dip. Elettronica, Politecnico di Milano, Italy (1992)

    Google Scholar 

  3. Dorigo, M., Blum, C.: Ant colony optimization: a survey. Theorical Computer Science 344, 243–278 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)

    MATH  Google Scholar 

  5. Orloff, C.S.: A fundamental problem in vehicle routing. Networks 4, 35–64 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lenstra, J.K., Rinnooy-Kan, A.H.G.: On general routing problems. Networks 6(3), 273–280 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  7. Eiselt, H.A., Gendreau, M., Laporte, G.: Arc routing problems, part II: The rural postman problem. Oper. Res. 43(3), 399–414 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Christofides, N., Campos, V., Corberán, A., Mota, E.: An algorithm for the rural postman problem. Tech. Rep. IC-O.R.-81-5, Imperial College, London, UK (1981)

    Google Scholar 

  9. Corberán, A., Sanchís, J.M.: A polyhedral approach to the rural postman problem. Eur. J. Oper. Res. 79, 95–114 (1994)

    Article  MATH  Google Scholar 

  10. Letchford, A.N.: Polyhedral results for some constrained arc routing problems. Ph.D. thesis, Lancaster University, Lancaster (1996)

    Google Scholar 

  11. Ghiani, G.: A branch-and-cut algorithm for the undirected rural postman problem. Math. Programming 87(3), 467–481 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chistofides, N., Campos, V., Corberán, A., Mota, E.: An algorithm for the rural postman problem on a directed graph. Math. Programming Stud. 26, 155–166 (1986)

    Google Scholar 

  13. Chistofides, N., Mingozzi, A., Toth, P.: Exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations. Math. Programming 20(1), 255–282 (1986)

    Article  Google Scholar 

  14. Fernández, E., Meza, O., Garfinkel, R., Ortega, M.: On the undirected rural postman problem: Tight bounds based on a new formulation. Oper. Res. 51(2), 281–291 (2003)

    Article  MathSciNet  Google Scholar 

  15. Fernández, P., García, L.M., Sanchis, J.M.: A heuristic algorithm based on Monte Carlo methods for the rural postman problem. Comput. Oper. Res. 25(12), 1097–1106 (1998)

    Article  MATH  Google Scholar 

  16. Frederickson, G.N.: Approximation algorithms for some postman problems. J. ACM 26(3), 538–554 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ghiani, G., Laganà, D., Musmanno, R.: A constructive heuristic for the undirected rural postman problem. Comput. Oper. Res. 33(12), 3450–3457 (2006)

    Article  MATH  Google Scholar 

  18. Groves, G.W., van Vuure, J.H.: Efficient heuristics for the rural postman problem. Orion 21(1), 33–51 (2005)

    Google Scholar 

  19. Hertz, A., Laporte, G., Nanchen-Hugo, P.: Improvement procedures for the undirected rural postman problem. INFORMS J. Comput. 11(1), 53–62 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pearn, W.L., Wu, T.C.: Algorithms for the rural postman problem. Comput. Oper. Res. 22(8), 819–828 (1995)

    Article  MATH  Google Scholar 

  21. Baldoquín, M.G.: Heuristics and metaheuristics approaches used to solve the rural postman problem: a comparative case study. In: Proc. Fourth Internat. ICSC Symposium on Engineering of Intelligent Systems (EIS 2004), Maderia, Portugal (2004)

    Google Scholar 

  22. Baldoquín, M.G., Ryan, G., Rodriguez, R., Castellini, A.: Un enfoque híbrido basado en metaheurísticas para el problema del cartero rural. In: Proc. of XI CLAIO, Concepci’on de Chile, Chile (2002)

    Google Scholar 

  23. Kang, M.J., Han, C.G.: Solving the rural postman problem using a genetic algorithm with a graph transformation. Tech. rep., Dept. of Computer Engineering, Kyung Hee University (1998)

    Google Scholar 

  24. Pérez-Delgado, M.L.: A solution to the rural postman problem based on artificial ant colonies. In: Borrajo, D., Castillo, L., Corchado, J.M. (eds.) CAEPIA 2007. LNCS (LNAI), vol. 4788, pp. 220–228. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  25. Pérez-Delgado, M.L., Matos-Franco, J.C.: Self-organizing feature maps to solve the undirected rural postman problem. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds.) EUROCAST 2007. LNCS, vol. 4739, pp. 804–811. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  26. Rodrigues, A.M., Ferreira, J.S.: Solving the rural postman problem by memetic algorithms. In: MIC 2001 - 4TH Metaheuristics Internat. Conf., Porto, Portugal (2001)

    Google Scholar 

  27. Stützle, T., Hoos, H.: The MAX-MIN Ant System and local search for the traveling salesman problem. In: Bäck, T., Michalewicz, Z., Yao, X. (eds.) Proc. IEEE Internat. Conf. on Evolutionary Computation, pp. 309–314 (1997)

    Google Scholar 

  28. Stützle, T., Dorigo, M.: A short convergence proof for a class of ant colony optimization algorithms. IEEE Trans. Evol. Comput. 6(4), 358–365 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pérez-Delgado, M.L. (2009). The Undirected Rural Postman Problem Solved by the MAX-MIN Ant System. In: Demazeau, Y., Pavón, J., Corchado, J.M., Bajo, J. (eds) 7th International Conference on Practical Applications of Agents and Multi-Agent Systems (PAAMS 2009). Advances in Intelligent and Soft Computing, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00487-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00487-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00486-5

  • Online ISBN: 978-3-642-00487-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics