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A Bidirectional Building Approach for the 2D Guillotine Knapsack Packing Problem

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Recent Trends in Applied Artificial Intelligence (IEA/AIE 2013)

Abstract

We investigate the 2D guillotine knapsack packing problem, where the objective is to select and pack a set of rectangles into a sheet with fix size and maximize the total profit of packed rectangles. We combine well known two methods namely top-down approach and bottom-up approach into a coherent algorithm to address this problem. Computational experiments on benchmark test sets show that our approach could find optimal solution for almost all the instances with moderate size and outperform all existing approaches for the larger instances.

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References

  1. Christofides, N., Whitlock, C.: An algorithm for two-dimensional cutting problems. Operations Research 25(1), 30–44 (1977)

    Article  MATH  Google Scholar 

  2. Wang, P.Y.: Two algorithms for constrained two-dimensional cutting stock problems. Operations Research 31(3), 573–586 (1983)

    Article  MATH  Google Scholar 

  3. Viswanathan, K.V., Bagchi, A.: Best-first search methods for constrained two-dimensional cutting stock problems. Operations Research 41(4), 768–776 (1993)

    Article  MATH  Google Scholar 

  4. Hifi, M.: An improvement of Viswanathan and Bagchi’s exact algorithm for constrained two-dimensional cutting stock. Computers & Operations Research 24(8), 727–736 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cung, V.D., Hifi, M., Le Cun, B.: Constrained two-dimensional cutting stock problems a best-first branch-and-bound algorithm. International Transactions in Operational Research 7(3), 185–210 (2000)

    Article  MathSciNet  Google Scholar 

  6. Yoon, K., Ahn, S., Kang, M.K.: An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems. International Journal of Production Research, 1–14 (June, October 2012)

    Google Scholar 

  7. Dolatabadi, M., Lodi, A., Monaci, M.: Exact algorithms for the two-dimensional guillotine knapsack. Computers & Operations Research 39(1), 48–53 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hifi, M.: Dynamic programming and hill-climbing techniques for constrained two-dimensional cutting stock problems. Journal of Combinatorial Optimization 8, 65–84 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hopper, E., Turton, B.C.H.: An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research 128(1), 34–57 (2001)

    Article  MATH  Google Scholar 

  10. Bortfeldt, A., Winter, T.: A genetic algorithm for the two-dimensional knapsack problem with rectangular pieces. International Transactions in Operational Research 16(6), 685–713 (2009)

    Article  MATH  Google Scholar 

  11. Beasley, J.E.: A population heuristic for constrained two-dimensional non-guillotine cutting. European Journal of Operational Research 156(3), 601–627 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, Y.: A recursive algorithm for constrained two-dimensional cutting problems. Computational Optimization and Applications 41(3), 337–348 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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© 2013 Springer-Verlag Berlin Heidelberg

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Wei, L., Lim, A., Zhu, W. (2013). A Bidirectional Building Approach for the 2D Guillotine Knapsack Packing Problem. In: Ali, M., Bosse, T., Hindriks, K.V., Hoogendoorn, M., Jonker, C.M., Treur, J. (eds) Recent Trends in Applied Artificial Intelligence. IEA/AIE 2013. Lecture Notes in Computer Science(), vol 7906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38577-3_24

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  • DOI: https://doi.org/10.1007/978-3-642-38577-3_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38576-6

  • Online ISBN: 978-3-642-38577-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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