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Monte Carlo study of the sphere packing problem

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  • Li, S.P
  • Ng, Ka-Lok

Abstract

We employ the Monte Carlo method to study a constrained optimization problem, that is packing spheres with unequal radii into a 3-D bounded region. Selection of the best fit solution is based on using the Boltzmann factor, e−ΔE/T to determine the transition probability, which allows us to search for the global optimal solution. We determined the least numbers of packed spheres that will occupy the largest volume. The optimal occupied volume found is around 44% of a bounded region volume, which is obtained within a relative short computing time. This suggests that our result could be able to give a good starting point for the radiosurgery treatment plan.

Suggested Citation

  • Li, S.P & Ng, Ka-Lok, 2003. "Monte Carlo study of the sphere packing problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(1), pages 359-363.
    • Handle: RePEc:eee:phsmap:v:321:y:2003:i:1:p:359-363
    DOI: 10.1016/S0378-4371(02)01798-3
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    References listed on IDEAS

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    1. Jie Wang, 1999. "Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 453-463, December.
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    Cited by:

    1. Yeboah, S.K. & Darkwa, J., 2016. "A critical review of thermal enhancement of packed beds for water vapour adsorption," Renewable and Sustainable Energy Reviews, Elsevier, vol. 58(C), pages 1500-1520.

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