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International Symposium on Parallel Architectures, Algorithms and Programming

PAAP 2019: Parallel Architectures, Algorithms and Programming pp 221–233Cite as

An Improved Heuristic-Dynamic Programming Algorithm for Rectangular Cutting Problem

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1163))

Abstract

In this paper, we discussed a two-dimensional cutting problem with defects. In this problem, we are given a rectangular area which contains defects. The objective is to cut some rectangles with a given shape and direction from this rectangular area, which cannot overlap the defects, maximizing some profit associated with the rectangles generating by this cutting. We present an improved Heuristic-Dynamic Program (IHDP) to solve this problem and prove the important theorem about its complexity. The algorithm reduces the size of the discretization sets, establishes one-dimensional knapsack problem with the width and height of the small rectangular blocks, constructs two discretization sets using the obtained solution and the right and upper boundaries of the defects, and performs trial cut lines for each element of the discretization set. The algorithm calculates 14 internationally recognized examples. The experimental results show that it obtains the optimal solution of these examples, and its computing time is nearly ten times higher than that of the latest literature algorithm.

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References

  1. Liu, Y., Chu, C., Wang, K.: A new heuristic algorithm for a class of two-dimensional bin-packing problems. Int. J. Adv. Manuf. Technol. 57(9–12), 1235–1244 (2011)

    Article  Google Scholar 

  2. Clautiaux, F., Jouglet, A., Hayek, J.E.: A new lower bound for the non-oriented two-dimensional bin-packing problem. Oper. Res. Lett. 35(3), 365–373 (2007)

    Article  MathSciNet  Google Scholar 

  3. Zhang, D., Han, S.H., Ye, W.G.: A bricklaying heuristic algorithm for the orthogonal rectangular packing problem. Chin. J. Comput. 31(3), 509–515 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Lei, W., Qiang, L., Xin, C.: Heuristic search algorithm for the rectangular fixed-size guillotine bin packing problem. J. Softw. 28, 1640–1654 (2017)

    MathSciNet  MATH  Google Scholar 

  6. Cui, Y.D.: Recursive algorithm for generating optimal T-shape cutting patterns of rectangular blanks. J. Comput. Aided Des. Comput. Graph. 18(1), 125 (2006)

    Google Scholar 

  7. Song, X., Chu, C.B., Lewis, R., et al.: A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting. Eur. J. Oper. Res. 202(2), 368–378 (2010)

    Article  Google Scholar 

  8. Yoon, K., Ahn, S., Kang, M.: An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems. Int. J. Prod. Res. 51(6), 1680–1693 (2013)

    Article  Google Scholar 

  9. Herz, J.C.: Recursive computational procedure for two-dimensional stock cutting. IBM J. Res. Dev. 16(5), 462–469 (1972)

    Article  MathSciNet  Google Scholar 

  10. Beasley, J.E.: Algorithms for unconstrained two-dimensional guillotine cutting. J. Oper. Res. Soc. 36(4), 297–306 (1985)

    Article  Google Scholar 

  11. Carnieri, C., Mendoza, G.A., Luppold, W.G.: Optimal cutting of dimension parts from lumber with a defect: a heuristic solution procedure. For. Prod. J. 43, 66–72 (1993)

    Google Scholar 

  12. Vianna, A.C.G., Arenales, M.N.: Problema de corte de placas defeituosas. Pesqui Operacional 26, 185–202 (2006)

    Article  Google Scholar 

  13. Neidlein, V., Vianna, A.C.G., Arenales, M.N., Wäscher, G.: The two-dimensional guillotine-layout cutting problem with a single defect - an AND/OR-graph approach. Oper. Res. Proc., 85–90 (2008). Fleischmann, B., et al. (ed.). Springer-Verlag, Heidelberg

    Google Scholar 

  14. Zhang, D., Deng, A., Kang, Y.: A hybrid heuristic algorithm for the rectangular packing problem. Lect. Notes Comput. Sci. 3514, 783–791 (2005)

    Article  Google Scholar 

  15. Zhang, D.F., Kang, Y., Deng, A.: A new heuristic recursive algorithm for the strip rectangular packing problem. Comput. Oper. Res. 33(8), 2209–2217 (2006)

    Article  Google Scholar 

  16. Berkey, J.O., Wang, P.Y.: Two-dimensional finite bin-packing algorithms. J. Oper. Res. Soc. 38(5), 423–429 (1987)

    Article  Google Scholar 

  17. Alvarez-Valdes, R., Martí, R., Tamarit, J.M., et al.: GRASP and path relinking for the two-dimensional two-stage cutting-stock problem. INFORMS J. Comput. 19(2), 261–272 (2007)

    Article  MathSciNet  Google Scholar 

  18. Afsharian, M., Niknejad, A., Wäscher, G.: A heuristic, dynamic programming-based approach for a two-dimensional cutting problem with defects. OR Spectrum 36(4), 971–999 (2014)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61862027, 61702238 and 61866014), the Natural Science Foundation Project of Jiangxi (Grant No. 20192BAB207008), the Science Foundation of Educational Commission of Jiangxi Province (Grant Nos. Gjj170316 and Gjj180264).

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Authors and Affiliations

  1. School of Software and Internet of Things Engineering, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China

    Aihua Yin, Chong Chen, Dongping Hu, Jianghai Huang & Fan Yang

Authors
  1. Aihua Yin
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  2. Chong Chen
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  3. Dongping Hu
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  4. Jianghai Huang
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  5. Fan Yang
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Corresponding author

Correspondence to Dongping Hu .

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Editors and Affiliations

  1. Sun Yat-sen University, Guangzhou, China

    Hong Shen

  2. Sun Yat-sen University, Guangzhou, China

    Yingpeng Sang

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Yin, A., Chen, C., Hu, D., Huang, J., Yang, F. (2020). An Improved Heuristic-Dynamic Programming Algorithm for Rectangular Cutting Problem. In: Shen, H., Sang, Y. (eds) Parallel Architectures, Algorithms and Programming. PAAP 2019. Communications in Computer and Information Science, vol 1163. Springer, Singapore. https://doi.org/10.1007/978-981-15-2767-8_21

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  • DOI: https://doi.org/10.1007/978-981-15-2767-8_21

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-2766-1

  • Online ISBN: 978-981-15-2767-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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