A Multi-sphere Scheme for 2D and 3D Packing Problems

  • Takashi Imamichi
  • Hiroshi Nagamochi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4638)


In this paper, we deal with a packing problem that asks to place a given set of objects such as non-convex polytopes compactly in ℝ2 and ℝ3, where we treat translation, rotation and deformation as possible motions of each object. We propose a multi-sphere scheme that approximates each object with a set of spheres to find a compact layout of the original objects. We focus on the case that all objects are rigid, and develop an efficient local search algorithm based on a nonlinear program formulation.


packing problem multi-sphere scheme iterated local search unconstrained nonlinear program 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Takashi Imamichi
    • 1
  • Hiroshi Nagamochi
    • 1
  1. 1.Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, KyotoJapan

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