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Evolving Bin Packing Heuristics with Genetic Programming

  • E. K. Burke
  • M. R. Hyde
  • G. Kendall
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)

Abstract

The bin-packing problem is a well known NP-Hard optimisation problem, and, over the years, many heuristics have been developed to generate good quality solutions. This paper outlines a genetic programming system which evolves a heuristic that decides whether to put a piece in a bin when presented with the sum of the pieces already in the bin and the size of the piece that is about to be packed. This heuristic operates in a fixed framework that iterates through the open bins, applying the heuristic to each one, before deciding which bin to use. The best evolved programs emulate the functionality of the human designed ‘first-fit’ heuristic. Thus, the contribution of this paper is to demonstrate that genetic programming can be employed to automatically evolve bin packing heuristics which are the same as high quality heuristics which have been designed by humans.

Keywords

Genetic Programming Timetabling Problem Piece Size Genetic Programming System Legal Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. The MIT Press, Cambridge, Massachusetts (1994)zbMATHGoogle Scholar
  2. 2.
    Koza, J.R., Bennett III, F.H., Andre, D., Keane, M.A.: Genetic Programming III: Darwinian Invention and Problem solving. Morgan Kaufmann, San Francisco (1999)zbMATHGoogle Scholar
  3. 3.
    Koza, J.R.: Genetic Programming: on the Programming of Computers by Means of Natural Selection. The MIT Press, Boston, Massachusetts (1992)zbMATHGoogle Scholar
  4. 4.
    Ross, P.: Hyper-heuristics. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 529–556. Kluwer, Boston (2005)Google Scholar
  5. 5.
    Burke, E.K., Hart, E., Kendall, G., Newall, J., Ross, P., Schulenburg, S.: Hyper-heuristics: An emerging direction in modern search technology. In: Glover, F., Kochenberger, G. (eds.) Handbook of Meta-Heuristics, pp. 457–474. Kluwer, Dordrecht (2003)Google Scholar
  6. 6.
    Soubeiga, E.: Development and Application of Hyperheuristics to Personnel Scheduling. PhD thesis, Univesity of Nottingham, School of Computer Science (2003)Google Scholar
  7. 7.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 4, 67–82 (1997)CrossRefGoogle Scholar
  8. 8.
    Whitley, D., Watson, J.P.: Complexity theory and the no free lunch theorem. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 317–339. Kluwer, Boston (2005)Google Scholar
  9. 9.
    Ross, P., Schulenburg, S., Marin-Blazquez, J.G., Hart, E.: Hyper heuristics: Learning to combine simple heuristics in bin packing problems. In: Proceedings of the Genetic and Evolutionary Computation Conference 2002 (GECCO 2002), pp. 942–948 (2002)Google Scholar
  10. 10.
    Ross, P., Marin-Blazquez, J.G., Schulenburg, S., Hart, E.: Learning a procedure that can solve hard bin-packing problems: A new ga-based approach to hyperheurstics. In: Proceedings of the Genetic and Evolutionary Computation Conference 2003 (GECCO 2003), Chicago, Illinois, pp. 1295–1306 (2003)Google Scholar
  11. 11.
    Burke, E.K., Kendall, G., Landa Silva, J.D., O’Brien, R.F.J., Soubeiga, E.: An ant algorithm hyperheuristic for the project presentation scheduling problem. In: Proceedings of the Congress on Evolutionary Computation 2005 (CEC 2005), Edinburgh, U.K., vol. 3, pp. 2263–2270 (2005)Google Scholar
  12. 12.
    Burke, E.K., Kendall, G., Soubeiga, E.: A tabu-search hyper-heuristic for timetabling and rostering. Journal of Heuristics 9, 451–470 (2003)CrossRefGoogle Scholar
  13. 13.
    Cowling, P., Kendall, G., Soubeiga, E.: A hyperheuristic approach to scheduling a sales summit. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 176–190. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Burke, E.K., Landa Silva, J.D., Soubeiga, E.: Multi-objective hyper-heuristic approaches for space allocation and timetabling. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Meta-heuristics: Progress as Real Problem Solvers, Selected Papers from the 5th Metaheuristics International Conference (MIC 2003), pp. 129–158. Springer, Heidelberg (2005)Google Scholar
  15. 15.
    Burke, E.K., McCollum, B., Meisels, A., Petrovic, S., Qu, R.: A graph-based hyper heuristic for educational timetabling problems. European Journal of Operational Research (in press, to appear 2006, available online November 21, 2005)Google Scholar
  16. 16.
    Burke, E.K., Petrovic, S., Qu, R.: Case based heuristic selection for timetabling problems. Journal of Scheduling 9, 115–132 (2006)zbMATHCrossRefGoogle Scholar
  17. 17.
    Dowsland, K., Soubeiga, E., Burke, E.K.: A simulated annealing hyper-heuristic for determining shipper sizes. European Journal of Operational Research (in press, to appear 2006, available online November 29, 2005) (accepted)Google Scholar
  18. 18.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. John Wiley and Sons, Chichester (1990)zbMATHGoogle Scholar
  19. 19.
    Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. Journal of Heuristics 2, 5–30 (1996)CrossRefGoogle Scholar
  20. 20.
    Beasley, J.E.: Binpacking benchmark data, at the brunell university or-library. (Last modified: 07-09-2004) [accessed March 1, 2006], Available at: http://people.brunel.ac.uk/~mastjjb/jeb/orlib/binpackinfo.html
  21. 21.
    Coffman Jr., E.G., Galambos, G., Martello, S., Vigo, D.: Bin packing approximation algorithms: Combinatorial analysis. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, Kluwer, Dordrecht (1998)Google Scholar
  22. 22.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Fransisco (1979)zbMATHGoogle Scholar
  23. 23.
    Rhee, W.T., Talagrand, M.: On line bin packing with items of random size. Math. Oper. Res. 18, 438–445 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Johnson, D., Demers, A., Ullman, J., Garey, M., Graham, R.: Worst-case performance bounds for simple one-dimensional packaging algorithms. SIAM Journal on Computing 3, 299–325 (1974)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Koza, J.R., Poli, R.: Genetic programming. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 127–164. Kluwer, Boston (2005)Google Scholar
  26. 26.
    Bernstein, Y., Li, X., Ciesielski, V., Song, A.: Multiobjective parsimony enforcement for superior generalisation performance. In: Proceedings of the Congress for Evolutionary Computation 2004 (CEC 2004), Portland, Oregon, pp. 83–89 (2004)Google Scholar
  27. 27.
    Falkenauer, E., Delchambre, A.: A genetic algorithm for bin packing and line balancing. In: Proceedings of the IEEE 1992 Int. Conference on Robotics and Automation, Nice, France, pp. 1186–1192 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • E. K. Burke
    • 1
  • M. R. Hyde
    • 1
  • G. Kendall
    • 1
  1. 1.School of Computer Science and Information TechnologyThe University of NottinghamNottinghamUnited Kingdom (UK)

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