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Mathematical Problems in Engineering
Volume 2014, Article ID 548957, 10 pages
http://dx.doi.org/10.1155/2014/548957
Research Article

Dealing with Nonregular Shapes Packing

Graduate Program in Applied Informatics, University of Fortaleza (UNIFOR), Avenue Washington Soares 1321, Bl J Sl 30, 60811-905 Fortaleza, CE, Brazil

Received 11 April 2014; Accepted 7 June 2014; Published 8 July 2014

Academic Editor: Jer-Guang Hsieh

Copyright © 2014 Bonfim Amaro Júnior et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Wäscher, H. Haußner, and H. Schumann, “An improved typology of cutting and packing problems,” European Journal of Operational Research, vol. 183, no. 3, pp. 1109–1130, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. F. M. B. Toledo, M. A. Carravilla, C. Ribeiro, J. F. Oliveira, and A. M. Gomes, “The dotted-board model: a new MIP model for nesting irregular shapes,” International Journal of Production Economics, vol. 145, no. 2, pp. 478–487, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. P. R. Pinheiro and P. R. Oliveira, “A hybrid approach of bundle and Benders applied large mixed linear integer problem,” Journal of Applied Mathematics, vol. 2013, Article ID 678783, 11 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  4. P. R. Pinheiro, A. L. V. Coelho, A. B. de Aguiar, and T. O. Bonates, “On the concept of density control and its application to a hybrid optimization framework: investigation into cutting problems,” Computers & Industrial Engineering, vol. 61, no. 3, pp. 463–472, 2011. View at Publisher · View at Google Scholar
  5. B. K. Nielsen and A. Odgaard, “Fast neighborhood search for the nesting problem,” Tech. Rep. 03/03, Department of Computer Science, University of Copenhagen, 2003. View at Google Scholar
  6. B. A. Junior, P. R. Pinheiro, and R. D. Saraiva, “Tackling the irregular strip packing problem by hybridizing genetic algorithm and bottom-left heuristic,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '13), pp. 3012–3018, Cancun, Mexico, June 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. B. Amaro Jr., P. R. Pinheiro, and R. D. Saraiva, “A hybrid methodology for tackling the irregular strip packing problem,” in Proceedings of the 11th IFAC Workshop on Intelligent Manufacturing Systems (IMS '13), 11, pp. 396–401, May 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. A. M. Gomes and J. F. Oliveira, “Solving irregular strip packing problems by hybridising simulated annealing and linear programming,” European Journal of Operational Research, vol. 171, no. 3, pp. 811–829, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Jakobs, “On genetic algorithms for the packing of polygons,” European Journal of Operational Research, vol. 88, no. 1, pp. 165–181, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Burke and G. Kendall, “Applying evolutionary algorithms and the no fit polygon to the nesting problem,” in Proceedings of the International Conference on Artificial Intelligence, vol. 1, pp. 51–57, 1999.
  11. J. F. Oliveira, A. M. Gomes, and J. S. Ferreira, “T{OPOS}: a new constructive algorithm for nesting problems,” OR Spektrum: Quantitative Approaches in Management, vol. 22, no. 2, pp. 263–284, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. C. H. Leung, Y. Lin, and D. Zhang, “Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem,” Computers and Operations Research, vol. 39, no. 3, pp. 678–686, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Egeblad, B. K. Nielsen, and A. Odgaard, “Fast neighborhood search for two- and three-dimensional nesting problems,” European Journal of Operational Research, vol. 183, no. 3, pp. 1249–1266, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. J. A. Bennell and X. Song, “A beam search implementation for the irregular shape packing problem,” Journal of Heuristics, vol. 16, no. 2, pp. 167–188, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, University of Michigan Press, Oxford, UK, 1975. View at MathSciNet
  16. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, Mass, USA, 1989.
  17. B. S. Baker, E. G. Coffman, and R. L. Rivest, “Orthogonal packings in two dimensions,” SIAM Journal on Computing, vol. 9, no. 4, pp. 846–855, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. C. Art, “An approach to the two-dimensional irregular cutting stock problem,” Tech. Rep. 36.008, IBM Cambridge Centre, 1966. View at Google Scholar
  19. R. Dighe and M. J. Jakiela, “Solving pattern nesting problems with genetic algorithms employing task decomposition and contact detection,” Evolutionary Computation, vol. 3, no. 3, pp. 239–266, 1996. View at Google Scholar
  20. A. Albano and G. Sapuppo, “Optimal allocation of two-dimensional irregular shapes using heuristic search methods,” IEEE Transactions on Systems, Man and Cybernetics, vol. 10, no. 5, pp. 242–248, 1980. View at Publisher · View at Google Scholar · View at Scopus
  21. C. Bounsaythip and S. Maouche, “Irregular shape nesting and placing with evolutionary approach,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, vol. 4, pp. 3425–3430, October 1997. View at Scopus
  22. V. M. M. Marques, C. F. G. Bispo, and J. J. S. Sentieiro, “A system for the compactation of two-dimensional irregular shapes based on simulated annealing,” in Proceedings of the International Conference on Industrial Electronics, Control and Instrumentation (IECON '91), pp. 1911–1916, Kobe, Japan, November 1991. View at Scopus
  23. J. F. Gonçalves and M. G. C. Resende, “Biased random-key genetic algorithms for combinatorial optimization,” Journal of Heuristics, vol. 17, no. 5, pp. 487–525, 2011. View at Publisher · View at Google Scholar · View at Scopus