A heuristic algorithm for cube packing with time schedule

  • Wei Li
  • WenQi Huang
  • DongChen Jiang
  • XiangLong Liu
Research Papers


Packing problem has been proved to be an NP-hard problem. Many algorithms such as simulation annealing algorithm, genetic algorithm and other heuristic algorithms have been proposed to solve two-dimensional and three-dimensional packing problem. To solve the cube packing problem with time schedule, this paper first introduces some concepts such as packing level, space distance and average neighbor birth order and then proposes a greedy algorithm. The algorithm tries every feasible corner greedily to calculate the space utilization, packing level, space distance, average neighbor birth order of this placement, and chooses the best placement according to these criteria. Theoretical analysis indicates that the time complexity of this algorithm is O(A 2 B 2 C 2 T 2 n 5). The experiments show that the average space utilization of non-guillotine cutting test cases is 98.81%, and the average space utilization of guillotine cutting test cases achieves 99.87%. Furthermore, optimal solutions of more than half cases are achieved by this algorithm. The experimental results show that this algorithm can solve the problem of cube packing with time schedule effectively and efficiently.


cube packing problem time schedule packing level space distance average neighbor birth order 


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  1. 1.
    Beasley J E. A population heuristic for constrained two-dimensional non-guillotine cutting. Eur J Oper Res, 2004, 156: 601–627MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Huang W Q, Liu J F. A deterministic heuristic algorithm based on euclidian distance for solving the rectangles packing problem. Chinese J Comput, 2006, 29: 734–739Google Scholar
  3. 3.
    Teich J, Fekete S P, Schepers J. Compile-time optimization of dynamic hardware reconfigurations. In: Proc PDPTA, Las Vegas, USA, 1999. 1097–1103Google Scholar
  4. 4.
    Yuh P H, Yang C L, Chang Y W, et al. Temporal floorplanning using 3D-subTCG. In: Proc ASPDAC, Yokohama, Japan, 2004. 723–728Google Scholar
  5. 5.
    Huang WQ. Quasi-physical and quasi-social method for tackling NP-hard problems. In: Proceedings of the International Workshop on Discrete Mathematics and Algorithms, China. Jinan: Jinan University Press, 1994. 89–91Google Scholar
  6. 6.
    Huang W Q, Xu R C. Two personification strategies for solving circles packing problem. Sci China Ser F-Inf Sci, 1999, 42: 595–602MATHGoogle Scholar
  7. 7.
    Wu Y L, Huang W Q. An effective quasi-human based heuristic for solving the rectangle packing problem. Eur J Oper Res, 2002, 141: 341–358MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Zhou Z, Dong S Q, Hong X L, et al. A new approach based on LFF for optimization of dynamic hardware reconfigurations. In: Proc of IEEE Int Symposium on Circuits and Systems, Hong Kong, 2005. 1210–1213Google Scholar
  9. 9.
    Chen D B, Huang W Q. Greedy algorithm for rectangle-packing problem. Comput Eng, 2007, 33: 160–162Google Scholar
  10. 10.
    Huang W Q, Zhan S H. A quasi-physical method of solving packing problems. Math Rev Am Math Society, 1982, 82h: 52002Google Scholar

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Wei Li
    • 1
  • WenQi Huang
    • 2
  • DongChen Jiang
    • 1
  • XiangLong Liu
    • 1
  1. 1.State Key Laboratory of Software Development EnvironmentBeihang UniversityBeijingChina
  2. 2.School of Computer Science and TechnologyHuazhong University of Science and TechnologyWuhanChina

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