Clustering Bin Packing Instances for Generating a Minimal Set of Heuristics by Using Grammatical Evolution

  • 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 574)


Grammatical Evolution has been used to evolve heuristics for the Bin Packing Problem. It has been shown that the use of Grammatical Evolution can generate an heuristic for either one instances or a full instance set for this problem. In many papers the selection of instances for heuristics generation has been done randomly. The present work proposes a methodology to cluster bin packing instances and choose the instances to generate an heuristic for each cluster. The number of heuristics generated is based on the number of clusters. There were used only one instance by cluster. The results obtained were compared through non-parametric tests against the best known heuristics.


Grammatical Evolution Bin Packing Problem Heuristics 



Authors thanks the support received from Consejo Nacional de Ciencia y Tecnologia (CONACyT).The authors want to thank to Instituto Tecnológico de León (ITL) for the support to this research. Additionally they want to aknowledge the generous support from the Mexican National Council for Science and Technology (CONACyT) for this research project.


  1. 1.
    Feigenbaum, E.A., Feldman, J.: Computers and Thought. AAAI Press (1963)Google Scholar
  2. 2.
    Romanycia, M.H.J., Pelletier, F.J.: What is a heuristic? Comput. Intell. 1(1), 47–58 (1985)CrossRefGoogle Scholar
  3. 3.
    Glover, F.W.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13, 533–549 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York, NY, USA (1979)zbMATHGoogle Scholar
  5. 5.
    Koza, J.R.: Hierarchical genetic algorithms operating on populations of computer programs. In: IJCAI. pp. 768–774 (1989)Google Scholar
  6. 6.
    Burke, E.K., Hyde, M., Kendall, G.: Evolving bin packing heuristics with genetic programming. In: Runarsson, T., Beyer, H.G., Burke, E., Merelo-Guervós, J., Whitley, L., Yao, X. (eds.) Parallel Problem Solving from Nature—PPSN IX. Lecture Notes in Computer Science, vol. 4193, pp. 860–869. Springer, Berlin, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Ryan, C., Collins, J., Collins, J., O’Neill, M.: Grammatical evolution: Evolving programs for an arbitrary language. In: Proceedings of the First European Workshop on Genetic Programming, Lecture Notes in Computer Science 1391, pp. 83–95. Springer (1998)Google Scholar
  8. 8.
    M., O., A, B.: Grammatical differential evolution. In: International Conference on Artificial Intelligence (ICAI’06). CSEA Press, Las Vegas, Nevada (2006)Google Scholar
  9. 9.
    O’Neill, M., Brabazon, A.: Grammatical swarm: The generation of programs by social programming. Nat. Comput. 5(4), 443–462 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Togelius, J., Nardi, R.D., Moraglio, A.: Geometric pso + gp = particle swarm programming. IEEE Congress on Evolutionary Computation, pp. 3594–3600 (2008)Google Scholar
  11. 11.
    Moraglio, A., Silva, S.: Geometric differential evolution on the space of genetic programs. In: Esparcia-Alcázar, A., Ekárt, A., Silva, S., Dignum, S., Uyar, A. (eds.) Genetic Programming. Lecture Notes in Computer Science, vol. 6021, pp. 171–183. Springer, Berlin / Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Sotelo-Figueroa, M.A., Puga Soberanes, H.J., Martín Carpio, J., Fraire Huacuja, H.J., Reyes, C.L., Soria-Alcaraz, J.A.: Evolving bin packing heuristic using micro-differential evolution with indirect representation. In: Castillo, O., Melin, P., Kacprzyk, J. (eds.) Recent Advances on Hybrid Intelligent Systems, Studies in Computational Intelligence, vol. 451, pp. 349–359. Springer, Berlin, Heidelberg (2013)Google Scholar
  13. 13.
    Allen, S., Burke, E.K., Hyde, M., Kendall, G.: Evolving reusable 3d packing heuristics with genetic programming. In: Proceedings of the 11th Annual conference on Genetic and evolutionary computation. pp. 931–938. GECCO’09, ACM, New York (2009)Google Scholar
  14. 14.
    Fukunaga, A.S.: Evolving local search heuristics for sat using genetic programming. In: Genetic and Evolutionary Computation—GECCO 2004, Lecture Notes in Computer Science, vol. 3103, pp. 483–494. Springer Berlin, Heidelberg (2004)Google Scholar
  15. 15.
    Hyde, M.R., Burke, E.K., Kendall, G.: Automated code generation by local search. J. Oper. Res. Soc. 64(12), 1725–1741 (2013)CrossRefGoogle Scholar
  16. 16.
    Hyde, M.: A Genetic programming hyper-heuristic approach to automated packing. Ph.D. thesis, University of Nottingham (2010)Google Scholar
  17. 17.
    Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3(4), 299–325 (1974)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yao, A.C.C.: New algorithms for bin packing. J. ACM 27, 207–227 (1980)CrossRefzbMATHGoogle Scholar
  19. 19.
    Rhee, W.T., Talagrand, M.: On line bin packing with items of random size. Math. Oper. Res. 18(2), 438–445 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Coffman, E., Jr., Galambos, G., Martello, S., Vigo, D.: Bin Packing Approximation Algorithms: Combinatorial Analysis. Kluwer Academic Publishers (1998)Google Scholar
  21. 21.
    Kämpke, T.: Simulated annealing: Use of a new tool in bin packing. Ann. Oper. Res. 16, 327–332 (1988)CrossRefGoogle Scholar
  22. 22.
    Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. J. Heuristics 2, 5–30 (1996)CrossRefGoogle Scholar
  23. 23.
    Ponce-Pérez, A., Pérez-Garcia, A., Ayala-Ramirez, V.: Bin-packing using genetic algorithms. In: Proceedings of the 15th International Conference on Electronics, Communications and Computers (CONIELECOMP 2005). pp. 311–314. IEEE Computer Society, Los Alamitos, CA, USA (2005)Google Scholar
  24. 24.
    Schwerin, P., Wäscher, G.: The bin-packing problem: A problem generator and some numerical experiments with ffd packing and mtp. Int. Trans. Oper. Res. 4(5–6), 377–389 (1997)CrossRefzbMATHGoogle Scholar
  25. 25.
    O'Neill, M., Brabazon, A.: Measuring instance difficulty for combinatorial optimization problems. Comput. Oper. Res. 39(5), 875–889 (2012)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Sotelo-Figueroa, M., Puga Soberanes, H., Martin Carpio, J., Fraire Huacuja, H., Cruz Reyes, L., Soria-Alcaraz, J.: Evolving and reusing bin packing heuristic through grammatical differential evolution. In: Nature and Biologically Inspired Computing (NaBIC), 2013 World Congress on. pp. 92–98 (2013)Google Scholar
  27. 27.
    Derrac, J., García, S., Molina, S., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, pp. 3–18 (2011)Google Scholar
  28. 28.
    Garey, M.R., Johnson, D.S.: “Strong” np-completeness results: motivation, examples, and implications. J. ACM 25, 499–508 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Martello, S., Toth, P.: Knapsack Problems Algorithms and Computer Implementations. Wiley, New York (1990)zbMATHGoogle Scholar
  30. 30.
    Schoenfield, J.E.: Fast, exact solution of open bin packing problems without linear programming. Ph.D. thesis, US Army Space and Missile Defense Command, Huntsville, Alabama (2002)Google Scholar
  31. 31.
    Belov, G., Scheithauer, G.: A cutting plane algorithm for the one-dimensional cutting stock problem with multiple stock lengths. Eur. J. Oper. Res. 141, 274–294 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Beasley, J.: Or-library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41(11), 1069–1072 (1990)CrossRefGoogle Scholar
  33. 33.
    Scholl, A., Klein, R., Jürgens, C.: Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem. Comput. Oper. Res. 24(7), 627–645 (1997)CrossRefzbMATHGoogle Scholar
  34. 34.
    Alvim, A., Ribeiro, C., Glover, F., Aloise, D.: A hybrid improvement heuristic for the one-dimensional bin packing problem. J. Heuristics 10(2), 205–229 (2004)CrossRefGoogle Scholar
  35. 35.
    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 May 1992Google Scholar
  36. 36.
    Coffman, Jr., E.G., Garey, M.R., Johnson, D.S.: Approximation Algorithms for Bin Packing: A Survey. In: Hochbaum, D.S. (eds.) Approximation Algorithms for NP-hard Problems, pp. 46–93. PWS Publishing Co., Boston (1997)Google Scholar
  37. 37.
    Falkenauer, E.: Tapping the full power of genetic algorithm through suitable representation and local optimization: application to bin packing. In: Biethahn, J., Nissen, V. (eds.) Evolutionary Algorithms in Management Applications, pp. 167–182. Springer, Berlin (1995)CrossRefGoogle Scholar
  38. 38.
    Gent, I.: Heuristic solution of open bin packing problems. J. Heuristics 3(4), 299–304 (1998)CrossRefzbMATHGoogle Scholar
  39. 39.
    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)CrossRefGoogle Scholar
  40. 40.
    lan Fang, H., lan Fang, H., Ross, P., Ross, P., Corne, D., Corne, D.: A promising genetic algorithm approach to job-shop scheduling, rescheduling, and open-shop scheduling problems. In: Proceedings of the Fifth International Conference on Genetic Algorithms. pp. 375–382. Morgan Kaufmann (1993)Google Scholar
  41. 41.
    Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. CRC, 2nd. edn. (2000)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

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 Tecnológico de LeónLeónMexico
  2. 2.Instituto Tecnológico de Ciudad MaderoTamaulipasMexico

Personalised recommendations