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Scientific Programming
Volume 2016, Article ID 1682925, 11 pages
http://dx.doi.org/10.1155/2016/1682925
Research Article

Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

1DEI, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
2Departamento de Ingeniería Informática, Universidad de Santiago de Chile, 3659 Avenida Ecuador, 9170124 Santiago, Chile

Received 2 December 2015; Revised 2 February 2016; Accepted 16 February 2016

Academic Editor: Frédéric Saubion

Copyright © 2016 Carlos Contreras-Bolton et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. B. Kruskal, “On the shortest spanning subtree of a graph and the traveling salesman problem,” Proceedings of the American Mathematical Society, vol. 7, no. 1, pp. 48–50, 1956. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. C. Prim, “Shortest connection networks and some generalizations,” Bell System Technical Journal, vol. 36, no. 6, pp. 1389–1401, 1957. View at Publisher · View at Google Scholar
  3. P. C. Pop, Generalized Network Design Problems. Modeling and Optimization, De Gruyter, Berlin, Germany, 2012.
  4. Y.-S. Myung, C.-H. Lee, and D.-W. Tcha, “On the generalized minimum spanning tree problem,” Networks, vol. 26, no. 4, pp. 231–241, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  5. M. Dror, M. Haouari, and J. Chaouachi, “Generalized spanning trees,” European Journal of Operational Research, vol. 120, no. 3, pp. 583–592, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. B. Golden, S. Raghavan, and D. Stanojević, “Heuristic search for the generalized minimum spanning tree problem,” INFORMS Journal on Computing, vol. 17, no. 3, pp. 290–304, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. P. C. Pop, “A survey of different integer programming formulations of the generalized minimum spanning tree problem,” Carpathian Journal of Mathematics, vol. 25, no. 1, pp. 104–118, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. P. C. Pop, W. Kern, and G. Still, “A new relaxation method for the generalized minimum spanning tree problem,” European Journal of Operational Research, vol. 170, no. 3, pp. 900–908, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. P. C. Pop, The generalized minimum spanning tree problem [Ph.D. thesis], University of Twente, Enschede, The Netherlands, 2002.
  10. P. C. Pop, “New models of the generalized minimum spanning tree problem,” Journal of Mathematical Modelling and Algorithms, vol. 3, no. 2, pp. 153–166, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. C. S. Ferreira, L. S. Ochi, V. Parada, and E. Uchoa, “A GRASP-based approach to the generalized minimum spanning tree problem,” Expert Systems with Applications, vol. 39, no. 3, pp. 3526–3536, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ, USA, 1982. View at MathSciNet
  13. T. Öncan, J.-F. Cordeau, and G. Laporte, “A tabu search heuristic for the generalized minimum spanning tree problem,” European Journal of Operational Research, vol. 191, no. 2, pp. 306–319, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. C. Contreras-Bolton, G. Gatica, C. R. Barra, and V. Parada, “A multi-operator genetic algorithm for the generalized minimum spanning tree problem,” Expert Systems with Applications, vol. 50, pp. 1–8, 2016. View at Publisher · View at Google Scholar
  15. M. Haouari and J. S. Chaouachi, “Upper and lower bounding strategies for the generalized minimum spanning tree problem,” European Journal of Operational Research, vol. 171, no. 2, pp. 632–647, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. E.-G. Talbi, Metaheuristics: From Design to Implementation, John Wiley & Sons, London, UK, 2009.
  17. E. K. Burke, M. R. Hyde, G. Kendall, G. Ochoa, E. Özcan, and J. R. Woodward, “A classification of hyper-heuristic approaches,” in Handbook of Metaheuristics, M. Gendreau and J.-Y. Potvin, Eds., vol. 146, pp. 1–21, Springer US, 2010. View at Google Scholar
  18. E. K. Burke, M. Gendreau, M. Hyde et al., “Hyper-heuristics: a survey of the state of the art,” Journal of the Operational Research Society, vol. 64, no. 12, pp. 1695–1724, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection Complex Adaptive Systems, MIT Press, Cambridge, Mass, USA, 1992.
  20. J. R. Koza, Genetic Programming IV: Routine Human-Competitive Machine Intelligence, Kluwer Academic, Norwell, Mass, USA, 2003.
  21. D. E. Goldberg, “Sizing populations for serial and parallel genetic algorithms,” in Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 70–79, Fairfax, Va, USA, June 1989.
  22. S. Minton, “An analytic learning system for specializing heuristics,” in Proceedings of the 13th International Joint Conference on Artifical Intelligence—Volume 2, pp. 922–928, Chambéry, France, August-September 1993.
  23. E. K. Burke, M. R. Hyde, G. Kendall, and J. R. Woodward, “Automating the packing heuristic design process with genetic programming,” Evolutionary Computation, vol. 20, no. 1, pp. 63–89, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. E. K. Burke, B. McCollum, A. Meisels, S. Petrovic, and R. Qu, “A graph-based hyper-heuristic for educational timetabling problems,” European Journal of Operational Research, vol. 176, no. 1, pp. 177–192, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. J. A. Vázquez-Rodríguez and S. Petrovic, “A new dispatching rule based genetic algorithm for the multi-objective job shop problem,” Journal of Heuristics, vol. 16, no. 6, pp. 771–793, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. A. Nareyek, “Choosing search heuristics by non-stationary reinforcement learning,” in Metaheuristics, M. G. C. Resende, J. P. de Sousa, and A. Viana, Eds., pp. 523–544, Kluwer Academic Publishers, Norwell, Mass, USA, 2004. View at Google Scholar
  27. C. Contreras Bolton, G. Gatica, and V. Parada, “Automatically generated algorithms for the vertex coloring problem,” PLoS ONE, vol. 8, no. 3, Article ID e58551, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Parada, M. Sepúlveda, C. Herrera, and V. Parada, “Automatic generation of algorithms for the binary knapsack problem,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '13), pp. 3148–3152, IEEE, Cancún, Mexico, June 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. L. Parada, C. Herrera, M. Sepúlveda, and V. Parada, “Evolution of new algorithms for the binary knapsack problem,” Natural Computing, pp. 1–13, 2015. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Affenzeller, S. Winkler, S. Wagner, and A. Beham, Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications, Chapman & Hall/CRC, New York, NY, USA, 2009.
  31. Á. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing, Springer, Berlin, Germany, 2008.
  32. A. Menon, Frontiers of Evolutionary Computation, Kluwer Academic Publishers, Norwell, Mass, USA, 2004.
  33. R. Poli, W. B. Langdon, and N. F. Mcphee, A Field Guide to Genetic Programming, Lulu Enterprises, London, UK, 2008.
  34. F. Rothlauf, Representations for Genetic and Evolutionary Algorithms, Springer, Secaucus, NJ, USA, 2nd edition, 2006.
  35. A. V. Aho, M. S. Lam, R. Sethi, and J. D. Ullman, Compilers: Principles, Techniques, and Tools, Addison Wesley, 2nd edition, 2006.
  36. J. G. Siek, L. Lee, and A. Lumsdaine, The Boost Graph Library: User Guide and Reference Manual, Addison-Wesley Longman Publishing, Boston, Mass, USA, 2002.
  37. D. R. Musser and A. Saini, The STL Tutorial and Reference Guide: C++ Programming with the Standard Template Library, Addison Wesley Longman Publishing, Redwood City, Calif, USA, 1995.
  38. B. Hu, M. Leitner, and G. R. Raidl, “Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem,” Journal of Heuristics, vol. 14, no. 5, pp. 473–499, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  39. C. Feremans, M. Labbé, and G. Laporte, “The generalized minimum spanning tree problem: polyhedral analysis and branch-and-cut algorithm,” Networks, vol. 43, no. 2, pp. 71–86, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. M. Fischetti, J. J. Salazar González, and P. Toth, “The symmetric generalized traveling salesman polytope,” Networks, vol. 26, no. 2, pp. 113–123, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  41. G. di Tollo, F. Lardeux, J. Maturana, and F. Saubion, “An experimental study of adaptive control for evolutionary algorithms,” Applied Soft Computing, vol. 35, pp. 359–372, 2015. View at Google Scholar
  42. S. Luke and L. Panait, “A comparison of bloat control methods for genetic programming,” Evolutionary Computation, vol. 14, no. 3, pp. 309–344, 2006. View at Publisher · View at Google Scholar · View at Scopus
  43. L. Panait and S. Luke, “Alternative bloat control methods,” in Genetic and Evolutionary Computation—GECCO 2004, K. Deb, Ed., vol. 3103, pp. 630–641, Springer, Berlin, Germany, 2004. View at Google Scholar
  44. L. Dagum and R. Menon, “OpenMP: an industry standard API for shared-memory programming,” IEEE Computational Science and Engineering, vol. 5, no. 1, pp. 46–55, 1998. View at Publisher · View at Google Scholar