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A Heuristic Based Algorithm for the 2D Circular Strip Packing Problem

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Recent Advances in Computational Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 470))

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Abstract

This paper solves the strip packing problem (SPP) that consists in packing a set of circular objects into a rectangle of fixed width and unlimited length. The objective is to minimize the length of the rectangle that will contain all the objects such that no object overlaps another one. The proposed algorithm uses a look-ahead method combined with beam search and a restarting strategy. The particularity of this algorithm is that it can achieve good results quickly (faster than other known methods and algorithms) even when the number of objects is large. The results obtained on well-known benchmark instances from the literature show that the algorithm improves a lot of best known solutions.

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References

  1. Baltacioglu, E., Moore, J.T., Hill, R.R.: The distributor’s three-dimensional pallet-packing problem: a human intelligence-based heuristic approach. Int. J. Oper. Res. 1, 249–266 (2006)

    MATH  Google Scholar 

  2. Bortfeldt, A., Homberger, J.: Packing first, routing seconda heuristic for the vehicle routing and loading problem. Comput. Oper. Res. 40, 873–885 (2013)

    Article  Google Scholar 

  3. Castillo, I., Kampas, F.J., Pintér, J.D.: Solving circle packing problems by global optimization: Numerical results and industrial applications. Eur. J. Oper. Res. 191, 786–802 (2008)

    Article  MATH  Google Scholar 

  4. Conway, J.H., Sloane, N.J.A.: Sphere packings, lattices and groups. A Series of comprehensive studies in Mathematics, vol. 290, 703 pages. Springer (1999)

    Google Scholar 

  5. Lewis, R., Song, S., Dowsland, K., Thompson, J.: An investigation into two bin packing problems with ordering and orientation implications. Eur. J. Oper. Res. 213, 52–65 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Menon, S., Schrage, L.: Order allocation for stock cutting in the paper industry. Oper. Res. 50, 324–332 (2002)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  8. Huang, W.Q., Li, Y., Li, C.M., Xu, R.C.: New heuristics for packing unequal circles into a circular container. Comput. Oper. Res. 33, 2125–2142 (2006)

    Article  MATH  Google Scholar 

  9. Hifi, M., M’Hallah, R.: A dynamic adaptive local search algorithm for the circular packing problem. European J. Oper. Res. 183, 1280–1294 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Akeb, H., Hifi, M., M’Hallah, R.: A beam search based algorithm for the circular packing problem. Comput. Oper. Res. 36, 1513–1528 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Graham, R.L., Lubachevsky, B.D., Nurmela, K.J., Östergård, P.R.J.: Dense packings of congruent circles in a circle. Discrete Math. 181, 139–154 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, J., Xue, S., Liu, Z., Xu, D.: An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle. Comput. Ind. Eng. 57, 1144–1149 (2009)

    Article  Google Scholar 

  13. George, J.A., George, J.M., Lamar, B.W.: Packing different-sized circles into a rectangular container. Eur. J. Oper. Res. 84, 693–712 (1995)

    Article  MATH  Google Scholar 

  14. Stoyan, Y.G., Yaskov, G.N.: Mathematical model and solution method of optimization problem of placement of rectangles and circles taking into account special constraints. Int. Trans. Oper. Res. 5, 45–57 (1998)

    MATH  Google Scholar 

  15. Hifi, M., M’Hallah, R.: Approximate algorithms for constrained circular cutting problems. Comput. Oper. Res. 31, 675–694 (2004)

    Article  MATH  Google Scholar 

  16. Huang, W.Q., Li, Y., Akeb, H., Li, C.M.: Greedy algorithms for packing unequal circles into a rectangular container. J. Oper. Res. Soc. 56, 539–548 (2005)

    Article  MATH  Google Scholar 

  17. Birgin, E.G., Martinez, J.M., Ronconi, D.P.: Optimizing the packing of cylinders into a rectangular container: A nonlinear approach. Eur. J. Oper. Res. 160, 19–33 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kubach, T., Bortfeldt, A., Gehring, H.: Parallel greedy algorithms for packing unequal circles into a strip or a rectangle. Cent. Eur. J. Oper. Res. 17, 461–477 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Akeb, H., Hifi, M., Negre, S.: An augmented beam search-based algorithm for the circular open dimension problem. Comput. Ind. Eng. 61, 373–381 (2011)

    Article  Google Scholar 

  20. Huang, W.Q., Ye, T.: Greedy vacancy search algorithm for packing equal circles in a square. Oper. Res. Lett. 38, 378–382 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Specht, E.: High density packings of equal circles in rectangles with variable aspect ratio. Comput. Oper. Res. 40, 58–69 (2013)

    Article  MathSciNet  Google Scholar 

  22. Locatelli, M., Raber, U.: Packing equal circles in a square: a deterministic global optimization approach. Discrete Appl. Math. 122, 139–166 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. López, C.O., Beasley, J.E.: A heuristic for the circle packing problem with a variety of containers. Eur. J. Oper. Res. 214, 512–525 (2011)

    Article  MATH  Google Scholar 

  24. Birgin, E.G., Sobral, F.N.C.: Minimizing the object dimensions in circle and sphere packing problems. Comput. Oper. Res. 35, 2357–2375 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. Birgin, E.G., Gentil, J.M.: New and improved results for packing identical unitary radius circles within triangles, rectangles and strips. Comput. Oper. Res. 37, 1318–1327 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Ow, P.S., Morton, T.E.: Filtered beam search in scheduling. Int. J. Prod. Res. 26, 35–62 (1988)

    Article  Google Scholar 

  27. Akeb, H., Hifi, M.: Adaptive algorithms for circular cutting/packing problems. Int. J. Oper. Res. 6, 435–458 (2009)

    Article  MATH  Google Scholar 

  28. Akeb, H., Hifi, M.: Algorithms for the circular two-dimensional open dimension problem. Int. Trans. Oper. Res. 15, 685–704 (2008)

    Article  MathSciNet  Google Scholar 

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Akeb, H., Hifi, M., Lazure, D. (2013). A Heuristic Based Algorithm for the 2D Circular Strip Packing Problem. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 470. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00410-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-00410-5_5

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00409-9

  • Online ISBN: 978-3-319-00410-5

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