Annals of Operations Research

, Volume 179, Issue 1, pp 369–392 | Cite as

Generalized hyper-heuristics for solving 2D Regular and Irregular Packing Problems

  • H. Terashima-Marín
  • P. Ross
  • C. J. Farías-Zárate
  • E. López-Camacho
  • M. Valenzuela-Rendón


The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such a combination should outperform the single heuristics. This article presents a GA-based method that produces general hyper-heuristics that solve two-dimensional regular (rectangular) and irregular (convex polygonal) bin-packing problems. A hyper-heuristic is used to define a high-level heuristic that controls low-level heuristics. The hyper-heuristic should decide when and where to apply each single low-level heuristic, depending on the given problem state. In this investigation two kinds of heuristics were considered: for selecting the figures (pieces) and objects (bins), and for placing the figures into the objects. Some of the heuristics were taken from the literature, others were adapted, and some other variations developed by us. We chose the most representative heuristics of their type, considering their individual performance in various studies and also in an initial experimentation on a collection of benchmark problems. The GA included in the proposed model 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 for most of the cases. The testbed is composed of problems used in other similar studies in the literature. Some additional instances for the testbed were randomly generated.


Cutting Stock Packing Hyper-heuristics Evolutionary computation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bai, R., Burke, E. K., & Kendall, G. (2008). Heuristic, meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation. Journal of the Operational Research Society (to appear). Google Scholar
  2. Banzhaf, W., Nordin, P., Keller, R. E., & Francone, F. D. (1998). Genetic programming: an introduction. London: Morgan Kaufmann. Google Scholar
  3. Beasley, J. E. (2003). Operations research library. Collection of problems for 2D packing and cutting.
  4. Berkey, J. O., & Wang, P. Y. (1987). Two-dimensional finite bin packing algorithms. Journal of Operational Research Society, 38(5), 423–429. Google Scholar
  5. Burke, E., Hart, E., Kendall, G., Newall, J., Ross, P., & Schulenburg, S. (2003a). Hyper-heuristics: an emerging direction in modern research technology. In Handbook of metaheuristics (pp. 457–474). Dordrecht: Kluwer Academic. Google Scholar
  6. Burke, E. K., Kendall, G., & Soubeiga, E. (2003b). A tabu-search hyperheuistic for timetabling and rostering. Journal of Heuristics, 9(6), 451–470. CrossRefGoogle Scholar
  7. Burke, E. K., Hyde, M. R., & Kendall, G. (2006). Evolving bin packing heuristics with genetic programming. In 9th PPSN (pp. 860–869). Reykjavik. LNCS. Google Scholar
  8. Burke, E. K., McCollum, B., Meisels, A., Petrovic, S., & Qu, R. (2007). A graph-based hyperheuristic for timetabling problems. European Journal of the Operational Research, 176(1), 177–192. CrossRefGoogle Scholar
  9. Cheng, C. H., Fiering, B. R., & Chang, T. C. (1994). The cutting stock problem. A survey. International Journal of Production Economics, 36, 291–305. CrossRefGoogle Scholar
  10. Dowsland, K. A., Dowsland, W. B., & Bennell, J. A. (1998). Jostling for position: local improvement for irregular cutting patterns. Journal of the Operational Research Society, 49(6), 647–658. Google Scholar
  11. Dowsland, K. A., Vaid, S., & Dowsland, W. B. (2002). An algorithm for polygon placement using a bottom-left strategy. European Journal of Operational Research, 141(2), 371–381. CrossRefGoogle Scholar
  12. Dowsland, K., Herbert, E., Kendall, G., & Burke, E. (2006). Using the search bounds to enhance a genetic algorithms approach to two rectangle packing problems. European Journal of Operational Research, 168(2), 390–402. CrossRefGoogle Scholar
  13. Dowsland, K., Soubeiga, E., & Burke, E. K. (2007). A simulated annealing hyper-heuristic for determining shipper sizes. European Journal of the Operational Research, 179(3), 759–774. CrossRefGoogle Scholar
  14. Dyckhoff, H. (1990). A topology of cutting and packing problems. European Journal of Operational Research, 44, 145–159. CrossRefGoogle Scholar
  15. Fogel, D. B., Owens, L. A., & Walsh, M. (1966). Artificial intelligence through simulated evolution. New York: Wiley. Google Scholar
  16. Fujita, K., Akagji, S., & Kirokawa, N. (1993). Hybrid approach for optimal nesting using a genetic algorithm and a local minimisation algorithm. In Proceedings of the 19th annual ASME design automation conference, Part 1 (of 2) (Vol. 65, part 1, pp. 477–484). Albuquerque, NM, USA. Google Scholar
  17. Garey, M., & Johnson, D. (1979). Computers and intractability. New York: W. H. Freeman. Google Scholar
  18. Goldberg, D. (1989). Genetic algorithms in search, optimization and machine learning. Reading: Addison-Wesley. Google Scholar
  19. Goldberg, D., Korb, B., & Deb, K. (1989). Messy genetic algorithms: Motivation, analysis and first results. Complex Systems, 3, 493–530. Google Scholar
  20. Golden, B. L. (1976). Approaches to the cutting stock problem. AIIE Transactions, 8, 256–274. Google Scholar
  21. Hifi, M., & MHallah, R. (2002). A best-local position procedure-based heuristic for two-dimensional layout problems. Studia Informatica Universalis, International Journal on Informatics, 2(1), 33–56. Google Scholar
  22. Hifi, M., & MHallah, R. (2003). A hybrid algorithm for the two-dimensional layout problem: the cases of regular and irregular shapes. International Transactions in Operational Research, 10, 195–216. CrossRefGoogle Scholar
  23. Holland, J. (1975). Adaptation in natural and artificial systems. Ann Arbor: The University of Michigan Press. Google Scholar
  24. Hopper, E., & Turton, B. C. (2001a). An empirical investigation of metaheuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research, 128(1), 34–57. CrossRefGoogle Scholar
  25. Hopper, E., & Turton, B. C. (2001b). An empirical study of meta-heuristics applied to 2D rectangular bin packing. Studia Informatica Universalis, 2(1), 77–106. Google Scholar
  26. Jakobs, S. (1996). On genetic algorithms for the packing of polygons. European Journal of Operations Research, 88, 165–181. CrossRefGoogle Scholar
  27. Kantorovich, L. V. (1960). Mathematical methods of organizing and planning production. Management Science, 6, 366–422. CrossRefGoogle Scholar
  28. Kendall, G., Soubeiga, E., & Cowling, P. (2004). Choice function and random hyperheuristics. In N. Press (Ed.), 4th Asia-Pacific conference on simulated evolution and learning (pp. 667–671). Nanyang. Google Scholar
  29. Kröger, B. (1995). Guillotineable bin packing: A genetic approach. European Journal of Operational Research, 84(2), 645–661. CrossRefGoogle Scholar
  30. Liu, D., & Teng, H. (1999). An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangle. European Journal of Operations Research, 112, 413–419. CrossRefGoogle Scholar
  31. Marín-Blázquez, J. G., & Schulenburg, S. (2007). A hyper-heuristic framework for XCS: learning to create novel problem-solving algorithms constructed from simpler algorithmic ingredients. In P. L. Lanzi, W. Stolzmann, & S. W. Wilson (Eds.), Learning classifier systems (pp. 193–218). Berlin: Springer. CrossRefGoogle Scholar
  32. Martello, S., & Vigo, D. (1998). Exact solution of the two-dimensional finite bin packing problem. Management Science, 44(3), 388–399. CrossRefGoogle Scholar
  33. Poli, R., Woodward, J., & Burke, E. K. (2007). A histogram-matching approach to the evolution of bin packing strategies. In Proceedings of congress on evolutionary computation CEC2007 (pp. 3500–3507). Singapore. Google Scholar
  34. Rechenberg, I. (1973). Evolutionstrategie: optimierung technischer systeme nach prinzipien dier biolischen evolution. Stuttgart: Frommann-Holzboog. Google Scholar
  35. Reeves, C. (1996). Hybrid genetic algorithms for bin-packing and related problems. Annals of Operations Research, 63(3), 371–396. CrossRefGoogle Scholar
  36. Ross, P., Schulenburg, S., Blázquez, J. M., & Hart, E. (2002). Hyper-heuristics: learning to combine simple heuristics in bin-packing problems. In Proceedings of GECCO 2002 (pp. 942–948). Google Scholar
  37. Ross, P., Blázquez, J. M., Schulenburg, S., & Hart, E. (2003). 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). Google Scholar
  38. Schwefel, H. P. (1981). Numerical optimization of computer models. Chichester: Wiley. Google Scholar
  39. Terashima-Marín, H., Flores-Álvarez, E. J., & Ross, P. (2005a). 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). Google Scholar
  40. Terashima-Marín, H., Morán-Saavedra, A., & Ross, P. (2005b). 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
  41. Terashima-Marín, H., Farías-Zárate, C. J., Ross, P., & Valenzuela-Rendón, M. (2006). A GA-based method to produce generalized hyper-heuristics for the 2D-regular cutting stock problem. In Proceedings of the genetic and evolutionary computation conference 2006 (pp. 591–598). Google Scholar
  42. Uday, A., Goodman, E. D., & Debnath, A. A. (2001). Nesting of irregular shapes using feature matching and parallel genetic algorithms. In E.D. Goodman (Ed.), 2001 genetic and evolutionary computation conference late breaking papers (pp. 429–434). San Francisco, California, USA. Google Scholar
  43. Wilson, R. A., & Keil, F. C. (1999). The MIT encyclopedia of the cognitive science. Cambridge: MIT Press. Google Scholar
  44. Wäscher, G., Haussner, H., & Schumann, H. (2007). An improved typology of cutting and packing problems. European Journal of Operational Research, 183(3), 1109–1130. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • H. Terashima-Marín
    • 1
  • P. Ross
    • 2
  • C. J. Farías-Zárate
    • 1
  • E. López-Camacho
    • 1
  • M. Valenzuela-Rendón
    • 1
  1. 1.Tecnológico de MonterreyCenter for Intelligent Systems MonterreyNuevo LeónMexico
  2. 2.School of ComputingNapier UniversityEdinburghUK

Personalised recommendations