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Mathematical Problems in Engineering
Volume 2017, Article ID 1670709, 11 pages
https://doi.org/10.1155/2017/1670709
Research Article

A Parallel Biased Random-Key Genetic Algorithm with Multiple Populations Applied to Irregular Strip Packing Problems

Graduate Program in Applied Informatics, University of Fortaleza (UNIFOR), Av. Washington Soares, 1321 Bl J Sl 30, 60.811-905 Fortaleza, CE, Brazil

Correspondence should be addressed to Plácido Rogério Pinheiro; rb.rofinu@odicalp

Received 2 April 2017; Revised 6 July 2017; Accepted 1 August 2017; Published 17 September 2017

Academic Editor: Jorge Magalhaes-Mendes

Copyright © 2017 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 Scopus
  2. J. F. Oliveira, A. M. Gomes, and J. . Ferreira, “Topos–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
  3. 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
  4. A. K. Sato, T. C. Martins, and M. S. G. Tsuzuki, “An algorithm for the strip packing problem using collision free region and exact fitting placement,” CAD Computer Aided Design, vol. 44, no. 8, pp. 766–777, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Alvarez-Valdes, A. Martinez, and J. M. Tamarit, “A branch & bound algorithm for cutting and packing irregularly shaped pieces,” International Journal of Production Economics, vol. 145, no. 2, pp. 463–477, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. 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
  7. M. A. Carravilla, C. Ribeiro, and J. F. Oliveira, “Solving nesting problems with non-convex polygons by constraint logic programming,” International Transactions in Operational Research, vol. 10, no. 6, pp. 651–663, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. Fischetti and I. Luzzi, “Mixed-integer programming models for nesting problems,” Journal of Heuristics, vol. 15, no. 3, pp. 201–226, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. K. K. Daniels, V. J. Milenkovic, and Z. Li, “Multiple containment methods,” Tech. Rep., Center for Research in Computing Technology, Harvard University, Cambridge, UK, 1994. View at Google Scholar
  10. 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
  11. L. H. Cherri, M. A. Carravilla, and F. M. B. Toledo, “A model-based heuristic for the irregular strip packing problem,” Pesquisa Operacional, vol. 36, no. 3, pp. 447–468, 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Ribeiro and M. A. Carravilla, “A global constraint for nesting problems,” Artificial Intelligence Review, vol. 30, no. 1-4, pp. 99–118, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. B. K. Nielsen and A. Odgaard, “Fast neighborhood search for the nesting problem,” Sci. Report, University of Copenhagen, 2003. View at Google Scholar
  14. K. A. Dowsland and W. B. Dowsland, “Solution approaches to irregular nesting problems,” European Journal of Operational Research, vol. 84, no. 3, pp. 506–521, 1995. View at Publisher · View at Google Scholar · View at Scopus
  15. B. A. Junior, P. R. Pinheiro, and R. D. Saraiva, “A hybrid methodology for nesting irregular shapes: case study on a textile industry?” in Proceedings of the 6th IFAC/ACM Conference on Management and Control of Production and Logistics (MCPL '13), pp. 15–20, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. 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
  17. 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
  18. B. A. Junior, P. R. Pinheiro, R. D. Saraiva, and P. G. Dantas Pinheiro, “Dealing with nonregular shapes packing,” Mathematical Problems in Engineering, Article ID 548957, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. Ramesh Babu and N. Ramesh Babu, “A generic approach for nesting of 2-D parts in 2-D sheets using genetic and heuristic algorithms,” CAD Computer Aided Design, vol. 33, no. 12, pp. 879–891, 2001. View at Publisher · View at Google Scholar · View at Scopus
  20. A. M. Gomes and J. F. Oliveira, “A 2-exchange heuristic for nesting problems,” European Journal of Operational Research, vol. 141, no. 2, pp. 359–370, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. E. Burke, R. Hellier, G. Kendall, and G. Whitwell, “A new bottom-left-fill heuristic algorithm for the two-dimensional irregular packing problem,” Operations Research, vol. 54, no. 3, pp. 587–601, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. T. Imamichi, M. Yagiura, and H. Nagamochi, “An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem,” Discrete Optimization, vol. 6, no. 4, pp. 345–361, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. 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
  24. 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 MathSciNet · View at Scopus
  25. 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
  26. B. A. Júnior and P. R. Pinheiro, “Approaches to tackle the nesting problems,” Advances in Intelligent Systems and Computing, vol. 464, pp. 285–295, 2016. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Stoyan and L. Ponomarenko, “Minkowski sum and hodograph of the dense placement vector function,” Reports of the SSR Academy of Science, SER. A, vol. 10, 1977. View at Google Scholar
  28. P. Rocha, R. Rodrigues, F. M. B. Toledo, and A. M. Gomes, “Circle covering using medial axis,” in Proceedings of the 11th IFAC Workshop on Intelligent Manufacturing Systems (IMS '13), pp. 402–407, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. R. C. Art, “An approach to the two-dimensional irregular cutting stock problem,” Technical Report 36.008, IBM Cambridge Centre, 1966. View at Google Scholar
  30. M. Adamowicz and A. Albano, “A Solution of the Rectangular Cutting-Stock Problem,” IEEE Trans. Systems, Man, Cybernetics, vol. SMC-6, pp. 302–310, 1976. View at Google Scholar
  31. 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 Scopus
  32. E. Flato and Dan Halperin, “Robust and efficient construction of planar Minkowski sums,” in In Abstracts 16th European Workshop Comput. Geom, pp. 85–88, Ben-Gurion University of the Negev, 2000. View at Google Scholar
  33. P. K. Agarwal, E. Flato, and D. Halperin, “Polygon decomposition for efficient construction of Minkowski sums,” Computational Geometry: Theory and Applications, vol. 21, no. 1-2, pp. 39–61, 2002. View at Publisher · View at Google Scholar · View at Scopus
  34. D. H. Greene, “Computational Geometry,” in Adv. Comput. Res, F. P. Preparata, Ed., vol. 1, pp. 235–259, JAI Press, Greenwich, 1983. View at Google Scholar
  35. J. C. Bean, “Genetic algorithms and random keys for sequencing and optimization,” ORSA Journal on Computing, vol. 6, no. 2, pp. 154–160, 1994. View at Publisher · View at Google Scholar
  36. W. M. Spears and K. A. De Jong, “On the virtues of parameterized uniform crossover,” in Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 230–237, 1991.
  37. P. R. Pinheiro, A. J. Saraiva, and R. A. Saraiva, “A random-key genetic algorithm for solving the nesting problem,” International Journal of Computer Integrated Manufacturing, vol. 28, pp. 1–7, 2015. View at Google Scholar
  38. 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
  39. L. R. Mundim, M. Andretta, and T. A. de Queiroz, “A biased random key genetic algorithm for open dimension nesting problems using no-fit raster,” Expert Systems with Applications, vol. 81, pp. 358–371, 2017. View at Publisher · View at Google Scholar · View at Scopus
  40. ESICUP, 2016, http://paginas.fe.up.pt/~esicup/.
  41. A. Elkeran, “A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering,” European Journal of Operational Research, vol. 231, no. 3, pp. 757–769, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus