Two-Phase GA-Based Model to Learn Generalized Hyper-heuristics for the 2D-Cutting Stock Problem

  • Hugo Terashima-Marín
  • Cláudia J. Farías-Zárate
  • Peter Ross
  • Manuel Valenzuela-Rendón
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4140)


The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such combination should outperform the single heuristics. This paper presents a GA-based method that produces general hyper-heuristics that solve two-dimensional cutting stock problems. The GA uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyper-heuristics, when tested with a large set of benchmark problems, produce outstanding results (optimal and near-optimal) for most of the cases. The testebed is composed of problems used in other similar studies in the literature. Some additional instances of the testbed were randomly generated.


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  1. 1.
    Beasley, J.E.: Beasley operations research library. Collection of problems for 2D packing and cutting (2003)Google Scholar
  2. 2.
    Berkey, J.O., Wang, P.Y.: Two-dimensional finite bin packing algorithms. Journal of Operational Research Society 38, 423–429 (1987)zbMATHGoogle Scholar
  3. 3.
    Burke, E., Hart, E., Kendall, G., Newall, J., Ross, P., Schulenburg, S.: Hyperheuristics: An emerging direction in modern research technolology. In: Handbook of Metaheuristics, pp. 457–474. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  4. 4.
    Cheng, C.H., Fiering, B.R., Chang, T.C.: The cutting stock problem. a survey. International Journal of Production Economics 36, 291–305 (1994)CrossRefGoogle Scholar
  5. 5.
    Dyckhoff, H.: A topology of cuting and packing problems. European Journal of Operation Research 44, 145–159 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Garey, M., Johnson, D.: Computers and Intractability. W.H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  7. 7.
    Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, Reading (1989)zbMATHGoogle Scholar
  8. 8.
    Goldberg, D., Korb, B., Deb, K.: Messy genetic algorithms: Motivation, analysis and first results. Complex Systems, 93–130 (1989)Google Scholar
  9. 9.
    Golden, B.L.: Approaches to the cutting stock problem. AIIE Transactions 8, 256–274 (1976)MathSciNetGoogle Scholar
  10. 10.
    Holland, J.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)Google Scholar
  11. 11.
    Hopper, E., Turton, B.C.: An empirical study of meta-heuristics applied to 2D rectangular bin packing. Studia Informatica Universalis, 77–106 (2001)Google Scholar
  12. 12.
    Jakobs, S.: On genetic algorithms for the packing of polygons. European Journal of Operations Research 88, 165–181 (1996)zbMATHCrossRefGoogle Scholar
  13. 13.
    Kantorovich, L.V.: Mathematical methods of organizing and planning production. Management Science 6, 366–422 (1960)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Liu, D., Teng, H.: An improved bl-algorithm for genetic algorithm of the orthogonal packing of rectangle. European Journal of Operations Research 112, 413–419 (1999)zbMATHCrossRefGoogle Scholar
  15. 15.
    Martello, S., Vigo, D.: Exact solution of the two-dimensional finite bin packing problem. Dipartimento di Elettronica, Informatica e Sistematica (1998)Google Scholar
  16. 16.
    Ross, P., Blázquez, J.M., Schulenburg, S., Hart, E.: Learning a procedure that can solve hard bin-packing problems: A new ga-based approach to hyper-heuristics. In: Proceedings of GECCO 2003, pp. 1295–1306 (2003)Google Scholar
  17. 17.
    Ross, P., Schulenburg, S., Blázquez, J.M., Hart, E.: Hyper-heuristics: learning to combine simple heuristics in bin-packing problems. In: Proceedings of GECCO 2002, pp. 942–948 (2002)Google Scholar
  18. 18.
    Terashima-Marín, H., Flores-Álvarez, E.J., Ross, P.: Hyper-heuristics and classifier systems for solving 2D-regular cutting stock problems. In: Proceedings of the Genetic and Evolutionary Computation Conference 2005, pp. 637–643 (2005)Google Scholar
  19. 19.
    Terashima-Marín, H., Morán-Saavedra, A., Ross, P.: Forming hyper-heuristics with GAs when solving 2D-regular cutting stock problems. In: Proceedings of the Congress on Evolutionary Computation, pp. 1104–1110 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hugo Terashima-Marín
    • 1
  • Cláudia J. Farías-Zárate
    • 1
  • Peter Ross
    • 2
  • Manuel Valenzuela-Rendón
    • 1
  1. 1.Center for Intelligent SystemsTecnológico de MonterreyMonterrey, Nuevo LeónMexico
  2. 2.School of ComputingNapier UniversityEdinburghUK

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