Journal of Intelligent & Robotic Systems

, Volume 67, Issue 3–4, pp 185–199 | Cite as

Optimal Packing Configuration Design with Finite-Circle Method

  • Jihong ZhuEmail author
  • Weihong Zhang
  • Liang Xia
  • Qiao Zhang
  • David Bassir


The Finite-circle Method (FCM) is further developed to solve 2D and 3D packing optimization problems with system compactness and moment of inertia constraints here. Instead of using the real geometrical shape as in existing solutions, we approximate the components and the design domain with circles of variant radii. Such approximation makes it possible to transform the original problem into a basic packing problem of FCM approximated components. Meanwhile, the overlapping between different components can be easily avoided by limiting the distance between corresponding circles in terms of their radii. With this formulation, the FCM provides a general and systematic approach and makes gradient-based optimization algorithms applicable. Furthermore, FCM has been extended to 3D packing problems by simply replacing circles with spheres in this paper. Several examples designing the compactness and moment of inertia of the component systems are presented to show the effect of FCM.


Packing optimization Finite-circle method Overlapping Moment of inertia 

Mathematics Subject Classification (2010)



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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Jihong Zhu
    • 1
    Email author
  • Weihong Zhang
    • 1
  • Liang Xia
    • 1
  • Qiao Zhang
    • 1
  • David Bassir
    • 2
  1. 1.Laboratory of Engineering Simulation and Aerospace Computing (ESAC), The Key Laboratory of Contemporary Design & Integrated Manufacturing TechnologyNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Technical University of Belfort MontbeliardBelfort CedexFrance

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