Evolving Bin Packing Heuristic Using Micro-Differential Evolution with Indirect Representation

  • Marco Aurelio Sotelo-FigueroaEmail author
  • Héctor José Puga Soberanes
  • Juan Martín Carpio
  • Héctor J. Fraire Huacuja
  • Laura Cruz Reyes
  • Jorge Alberto Soria Alcaraz
Part of the Studies in Computational Intelligence book series (SCI, volume 451)


The development of low-level heuristics for solving instances of a problem is related to the knowledge of an expert. He needs to analyze several components from the problem instance and to think out an specialized heuristic for solving the instance. However if any inherent component to the instance gets changes, then the designed heuristic may not work as it used to do it. In this paper it is presented a novel approach to generated low-level heuristics; the proposed approach implements micro-Differential Evolution for evolving an indirect representation of the Bin Packing Problem. It was used the Hard28 instance, which is a well-known and referenced Bin Packing Problem instance. The heuristics obtained by the proposed approach were compared against the well know First-Fit heuristic, the results of packing that were gotten for each heuristic were analized by the statistic non-parametric test known as Wilcoxon Signed Rank test.


Differential Evolution Cutting Plane Algorithm Hard28 Instance Donor Vector Grammatical Evolution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belov, G., Scheithauer, G.: A Cutting Plane Algorithm for the One-Dimensional Cutting Stock Problem with Multiple Stock Lengths. European Journal of Operational Research 141, 274–294 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Burke, E.K., Hart, E., Kendall, G., Newall, J., Ross, P., Schulenbur, S.: Hyperheuristics: An emerging direction in modern search technology. In: Glover, F., Kochenberger, G. (eds.) Handbook of Meta-Heuristics, pp. 457–474. Kluwer (2003)Google Scholar
  3. 3.
    Burke, E.K., Hyde, M.R., Kendall, G.: Evolving Bin Packing Heuristics with Genetic Programming. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 860–869. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Burke, E.K., Kendall, G.: Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques. Springer (2006)Google Scholar
  5. 5.
    Coffman Jr., E.G., Johnson, D.S., Mcgeoch, L.A., Weber, R.R.: Bin Packing with Discrete Item Sizes Part II: Average-Case Behavior of FFD and BFD 13, 384–402 (1997) (in preparation)Google Scholar
  6. 6.
    Falkenauer, E., Delchambre, A.: A genetic algorithm for bin packing and line balancing. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 2, pp. 1186–1192 (1992)Google Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: “ Strong ” NP-Completeness Results: Motivation, Examples, and Implications. J. ACM 25, 499–508 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press (1975)Google Scholar
  9. 9.
    Luke, S.: Essentials of Metaheuristics. Lulu (2009)Google Scholar
  10. 10.
    Martello, S., Toth, P.: Knapsack Problems, Algorithms and and Computer Implementations. John Wiley & Sons Ltd., New York (1990)zbMATHGoogle Scholar
  11. 11.
    Parsopoulos, K.E.: Cooperative micro-differential evolution for high-dimensional problems. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation in GECCO 2009, pp. 531–538. ACM, New York (2009)CrossRefGoogle Scholar
  12. 12.
    Ryan, C., Collins, J.J., Neill, M.O.: Grammatical Evolution: Evolving Programs for an Arbitrary Language. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 83–95. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Schoenfield, J.E.: Fast, exact solution of open bin packing problems without linear programming. PhD thesis. US Army Space and Missile Defense Command, Huntsville, Alabama, USA (2002)Google Scholar
  14. 14.
    Soubeiga, E.: Development and application of hyperheuristics to personnel scheduling. PhD thesis, University of Nottingham (2003)Google Scholar
  15. 15.
    Storn, R., Price, K.: Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. J. of Global Optimization 11, 341–359 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Yang, X.S.: Nature Inspired Metaheuristic Algorithms, 2nd edn. Luniver Press (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Marco Aurelio Sotelo-Figueroa
    • 1
    Email author
  • Héctor José Puga Soberanes
    • 1
  • Juan Martín Carpio
    • 1
  • Héctor J. Fraire Huacuja
    • 2
  • Laura Cruz Reyes
    • 2
  • Jorge Alberto Soria Alcaraz
    • 1
  1. 1.Instituto Tecnologico de LeónLeónMéxico
  2. 2.Instituto Tecnologico de Ciudad MaderoCiudad MaderoMéxico

Personalised recommendations