Advertisement

An ILS-Based Metaheuristic for the Stacker Crane Problem

  • Thais Ávila
  • Ángel Corberán
  • Isaac Plana
  • José M. Sanchis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7245)

Abstract

In this paper we propose a metaheuristic algorithm for the Stacker Crane Problem. This is an NP-hard arc routing problem whose name derives from the practical problem of operating a crane. Here we present a formulation and a lower bound for this problem and propose a metaheuristic algorithm based on the combination of a Multi-start and an Iterated Local Search procedures. Computational results on a large set of instances are presented.

Keywords

combinatorial optimization metaheuristics directed rural postman problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Belenguer, J.M., Benavent, E., Labadi, N., Prins, C., Reghioui, M.: Split Delivery Capacitated Arc Routing Problem: Lower Bound and Metaheuristic. Transportation Science 44, 206–220 (2010)CrossRefGoogle Scholar
  2. 2.
    Benavent, E., Corberán, A., Sanchis, J.M.: A metaheuristic for the min−max windy rural postman problem with K vehicles. Computational Management Science 7, 269–287 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Berbeglia, G., Cordeau, J.F., Gribkovskaia, I., Laporte, G.: Static pickup and delivery problems: a classification scheme and survey. TOP 15, 1–31 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Christofides, N.: Worst-case analysis of a new heuristic for the traveling salesman problem. Graduate School of Industrial Administration, Carnegie Mellon University (1976)Google Scholar
  5. 5.
    Cirasella, J., Johnson, D.S., McGeoch, L.A., Zhang, W.: The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests. In: Buchsbaum, A.L., Snoeyink, J. (eds.) ALENEX 2001. LNCS, vol. 2153, pp. 32–59. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Eiselt, H.A., Gendreau, M., Laporte, G.: Arc Routing Problems, Part II: The Rural Postman Problem. Operations Research 43, 399–414 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Frederickson, G.N., Hecht, M.S., Kim, C.E.: Aproximation Algorithms for some routing problems. SIAM Journal on Computing 7, 178–193 (1978)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Guan, M.: Graphic programming using odd or even points. Chinese Mathematics 1, 237–277 (1962)Google Scholar
  9. 9.
    Hassin, R., Khuller, S.: z-Approximations. Journal of Algorithms 41, 429–442 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Hertz, A., Laporte, G., Nachen-Hugo, P.: Improvement procedures for the undirected rural postman problem. INFORMS Journal on Computing 11, 53–62 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Laporte, G.: Modeling and solving several classes of arc routing problems as traveling salesman problems. Computers & Operations Research 24, 1057–1061 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Lenstra, J.K., Rinnooy Kan, A.H.G.: On general routing problem. Networks 6, 273–280 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lourenço, H.R., Martin, O., Stützle, T.: Iterated Local Search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 321–353 (2002)Google Scholar
  14. 14.
    Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers & Operations Research 24, 1097–1100 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Orloff, C.S.: A fundamental problem in vehicle routing. Networks 4, 35–64 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Srour, F.J.: Dissecting drayage: an examination if structure, information, and control in drayage operations. ERIM Ph.D. Series reseaarch in management, Erasmus Research Institute in Management, 1786 (2010) ISBN978-90-5892-226-7Google Scholar
  17. 17.
    Srour, F.J., van de Velde, S.: Are stacker crane problems easy? A statistical study. Computers & Operations Research (2011) doi:10.1016/j.cor.2011.06.017Google Scholar
  18. 18.
    Zhang, L.: Simple Heuristics for some variants on the traveling salesman problem. In: IEEE International Conference on Systems, Man and Cybernetics, vol. 2, pp. 1175–1178 (1992)Google Scholar
  19. 19.
    Zhang, L., Zheng, W.: Genetic coding for solving both the stacker crane problem and its k-variant. In: IEEE International Conference on Systems, Man and Cybernetics 1995, pp. 1061–1066 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thais Ávila
    • 1
  • Ángel Corberán
    • 1
  • Isaac Plana
    • 2
  • José M. Sanchis
    • 3
  1. 1.Dept. de Estadística e Investigación OperativaUniversitat de ValènciaSpain
  2. 2.Dept. Matemáticas para la Economía y la EmpresaUniversitat de ValènciaSpain
  3. 3.Dept. de Matemática AplicadaUniversidad Politécnica de ValenciaSpain

Personalised recommendations