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Optimal Packing Configuration Design with Finite-Circle Method

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Abstract

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.

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References

  1. Cagan, J., Shimada, K., Yin, S.: A survey of computational approaches to three-dimensional layout optimization. Comput. Aided Des. 34, 597–611 (2002)

    Article  Google Scholar 

  2. Fujita, K., Akagi, S., Hase, H.: Hybrid approaches to plant layout design using constraint directed search and an optimization technique.In: Proceedings of 17th ASME Design Automation Conference. 1, 131–138 (1991)

  3. Landon, M.D., Balling, R.J.: Optimal packaging of complex parametric solids according to mass property criteria. J. Mech. Des. 116, 375–381 (1994)

    Article  Google Scholar 

  4. De Bont, F.M.J., Aarts, E.H.L., Meehan, P., O’Brien, C.G.: Placement of shapeable blocks. Philips J. Res. 43, 1–22 (1988)

    Google Scholar 

  5. Pál, L.: A genetic algorithm for the two-dimensional single large object placement problem.In: Proceedings of 3rd Romanian-Hungarian Joint Symposium on Applied Computational Intelligence (2006)

  6. Huang, W.Q., Chen, D.B., Xu, R.C.: A new heuristic algorithm for rectangle packing. Comput. Oper. Res. 34, 3270–3280 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Clautiaux, F., Carlier, J., Moukrim, A.: A new exact method for the two-dimensional bin-packing problem with fixed orientation. Oper. Res. Lett. 35, 357–364 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Miyazawa, F.K., Wakabayashi, Y.: Two- and three-dimensional parametric packing. Comput. Oper. Res. 34, 2589–2603 (2007)

    Article  MATH  Google Scholar 

  9. Meagher, D.: Geometric modeling using octree encoding. Comput. Graph. Image Process. 19, 129–147 (1982)

    Article  Google Scholar 

  10. Samet, H.: Spatial Data Structures: Quadtree, Octree and Other Hierarchical Methods. Addison Wesley (1989)

  11. Moore, A.: The Circle Tree – A Hierarchical Structure for Efficient Storage, Access and Multi-scale Representation of Spatial Data. SIRC 2002, Dunedin, New Zealand (2002)

  12. Hubbard, P.M.: Interactive collision detection. Proceedings of IEEE Symposium on Research Frontiers in Virtual Reality (1993)

  13. Quinlan, S.: Efficient distance computation between non-convex objects.In: Proceedings of International Conference on Robotics and Automation 3324–3329 (1994)

  14. Cameron, S.: Approximation hierarchies and s-bounds. In: Proceedings Symposium on Solid modeling Foundations and CAD/CAM Applications 129–137 (1991)

  15. Cagan, J., Degentesh, D., Yin, S.: A simulated annealing-based algorithm using hierarchical models for general three-dimensional component layout. Comput. Aided Des. 30, 781–790 (1998)

    Article  MATH  Google Scholar 

  16. Lin, M., Gottschalk, S.: Collision detection between geometric models: a survey. In: Proceeding of IMA Conference on Mathematics of Surfaces (1998)

  17. Zhang, W.H., Zhang, Q.: Finite-circle method for component approximation and packing design optimization. Eng. Optim. 41, 971–987 (2009)

    Article  Google Scholar 

  18. Radovcic, Y., Remouchamps, A.: Boss Quattro: an open system for parametric design. Struct. Multidiscip. Optim. 23, 140–152 (2001)

    Article  Google Scholar 

  19. Svanberg, K.: A Globally Convergent Version of MMA Without Linesearch. First World Congress of Structural and Multidisciplinary Optimization. Pergamon, New York (1995)

    Google Scholar 

  20. Remouchamps, A., Radovcic, Y.: Boss-Quattro Documents. SAMTECH (2005)

  21. Nocedal, J., Wright, S.: Numerical Optimization. Springer, Series in Operations Research (1999)

  22. Fleury, C., Braibant, V.: Structural optimization: a new dual method using mixed variables. Int. J. Numer. Methods Eng. 23, 409–428 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Engineering Simulation and Aerospace Computing (ESAC), The Key Laboratory of Contemporary Design & Integrated Manufacturing Technology, Northwestern Polytechnical University, 710072, Xi’an, China

    Jihong Zhu, Weihong Zhang, Liang Xia & Qiao Zhang

  2. Technical University of Belfort Montbeliard, 90010, Belfort Cedex, France

    David Bassir

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  1. Jihong Zhu
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  2. Weihong Zhang
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  3. Liang Xia
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  4. Qiao Zhang
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  5. David Bassir
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Correspondence to Jihong Zhu.

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Zhu, J., Zhang, W., Xia, L. et al. Optimal Packing Configuration Design with Finite-Circle Method. J Intell Robot Syst 67, 185–199 (2012). https://doi.org/10.1007/s10846-011-9645-6

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  • DOI: https://doi.org/10.1007/s10846-011-9645-6

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