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Approaches to Tackle the Nesting Problems

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Artificial Intelligence Perspectives in Intelligent Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 464))

Abstract

The nesting problem arises in several manufacturing industries (e.g., furniture, garment, textile and wood). It is a representative cutting and packing problem in which a set of irregular polygons has to be placed within a rectangular container with a fixed width and a variable length to be minimized. We present a brief survey about the nesting problems in three different categories and its special approaches.

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References

  1. Albano, A., Sapuppo, G.: Optimal Allocation of Two-Dimensional Irregular Shapes Using Heuristic Search Methods. IEEE Trans. Sys. Man Cybern. SMC 10(5) (1980)

    Google Scholar 

  2. Alvarez-Valdes, R., Martinez, A., Tamarit, J.M.: A branch & bound algorithm for cutting and packing irregularly shaped pieces. Int. J. Prod. Econ. 145, 463–477 (2013)

    Article  Google Scholar 

  3. Amaro, Jr. B., Pinheiro, P.R., Saraiva, R.D.: Tackling the Irregular strip packing problem by hybridizing genetic algorithm and bottom-left heuristic. In: IEEE Congress on Evolutionary Computation (CEC), pp. 3012–3018 (2013)

    Google Scholar 

  4. Art, R.C.: An approach to the two-dimensional irregular cutting stock problem. Technical report 36.008, IBM Cambridge Centre (1966)

    Google Scholar 

  5. Baker, B.S., Coman, E.G., Rivest, R.L.: Orthogonal packing in two dimensions. SIAM J. Comput. 9(4), 846–855 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bennell, J.A., Song, X.: A beam search implementation for the irregular shape packing problem. J. Heuristics 16(2), 167–188 (2010)

    Article  MATH  Google Scholar 

  7. Burke, E., et al.: A new bottom-left-fill heuristic algorithm for the two-dimensional irregular packing problem. Oper. Res. 54(3), 587–601 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Carravilla, M.A., Ribeiro, C., Oliveira, J.F.: Solving nesting problems withnon-convex polygons by constraint logic programming. Int. Trans. Oper. Res. 10(6), 651–663 (2003). Blackwell Publishing Ltd.

    Google Scholar 

  9. Daniels, K.K., Milenkovic, V.J., Li, Z.: Multiple containment methods, Technical report 12–94, Center for Research in Computing Technology, Harvard University, Cambridge, MA (1994)

    Google Scholar 

  10. de Aguiar, A.B., Pinheiro, P.R., Coelho, Andre L.V.: On the concept of density control and its application to a hybrid optimization framework: investigation into cutting problems. Comput. Ind. Eng. 61, 463–472 (2011)

    Article  Google Scholar 

  11. Dowsland, K.A., Vaid, S., Dowsland, W.B.: An algorithm for polygon placement using a bottom-left strategy. Eur. J. Oper. Resour. 141, 371–381 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Egeblad, J., Nielsen, B.K., Odgaard, A.: Fast neighborhood search for twoand three-dimensional nesting problems. Eur. J. Oper. Res. 183(3), 1249–1266 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fischetti, M., Luzzi, I.: Mixed-integer programming models for nesting problems. J. Heuristics, Springer, US 15(3), 201–226 (2009)

    Article  MATH  Google Scholar 

  14. Fowler, R.J., Paterson, R.M., Tanimoto, S.T.: Optimal packing and covering in the plane are NP-complete. Inf. Process. Lett. 12, 133–137 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gomes, A.M., Oliveira, J.F.: Solving irregular strip packing problems by hybridizing simulated annealing and linear programming. Eur. J. Oper. Res. 171(3), 811–829 (2006)

    Article  MATH  Google Scholar 

  16. Hopper, E., Turton, B.: A genetic algorithm for a 2d industrial packing problem. Comput. Ind. Eng. 37(1–2), 375–378 (1999)

    Article  Google Scholar 

  17. Jakobs, S.: On genetic algorithms for the packing of polygons. Eur. J. Oper. Res. 88(1), 165–181 (1996)

    Article  MATH  Google Scholar 

  18. Leung, S.C., Lin, Y., Zhang, D.: Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem. Comput. Oper. Res. 39(3), 678–686 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Oliveira, J.F., Gomes, A.M., Ferreira, J.S.: TOPOS—A new constructive algorithm for nesting problems. OR-Spektrum 22(2), 263–284 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Amaro, Jr. B., Pinheiro, P.R., Saraiva, R.D.: Dealing with nonregular shapes packing. Math. Probl. Eng. (2014)

    Google Scholar 

  21. Pinheiro, P.R., Oliveira, P.R.: A hybrid approach of bundle and benders applied large mixed linear integer problem. J. Appl. Math. Article ID 678783, p. 11 (2013)

    Google Scholar 

  22. Toledo, F.M.B., Carravilla, M.A., Ribeiro, C., Oliveira, J.F., Miguel Gomes, A.: The Dotted-Board Model: a new MIP model for nesting irregular shapes. Int. J. Prod. Econ. 145, 478–487 (2013)

    Article  Google Scholar 

  23. Wäscher, G., HauBner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)

    Article  MATH  Google Scholar 

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Acknowledgments

The first author is thankful to Coordination for the Improvement of Higher Level or Education Personnel (CAPES) and the second author is thankful to National Counsel of Technological and Scientific Development (CNPq) via Grants #475,239/2012-1.

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Correspondence to Bonfim Amaro Júnior .

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Júnior, B.A., Pinheiro, P.R. (2016). Approaches to Tackle the Nesting Problems. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Silhavy, P., Prokopova, Z. (eds) Artificial Intelligence Perspectives in Intelligent Systems. Advances in Intelligent Systems and Computing, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-319-33625-1_26

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  • DOI: https://doi.org/10.1007/978-3-319-33625-1_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33623-7

  • Online ISBN: 978-3-319-33625-1

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