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An Attractor-Repeller approach to floorplanning

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  • Miguel F. Anjos
  • Anthony Vannelli

Abstract

The floorplanning (or facility layout) problem consists in finding the optimal positions for a given set of modules of fixed area (but perhaps varying height and width) within a facility such that the distances between pairs of modules that have a positive connection cost are minimized. This is a hard combinatorial optimization problem; even the restricted version where the shapes of the modules are fixed and the optimization is taken over a fixed finite set of possible module locations is NP-hard. In this paper, we extend the concept of target distance introduced by Etawil and Vannelli and apply it to derive the AR (Attractor-Repeller) model which is designed to improve upon the NLT method of van Camp et al. This new model is designed to find a good initial point for the Stage-3 NLT solver and has the advantage that it can be solved very efficiently using a suitable optimization algorithm. Because the AR model is not a convex optimization problem, we also derive a convex version of the model and explore the generalized target distances that arise in this derivation. Computational results demonstrating the potential of our approach are presented. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Miguel F. Anjos & Anthony Vannelli, 2002. "An Attractor-Repeller approach to floorplanning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(1), pages 3-27, August.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:1:p:3-27
    DOI: 10.1007/s001860200197
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    Citations

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    Cited by:

    1. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
    2. Anjos, Miguel F. & Vieira, Manuel V.C., 2017. "Mathematical optimization approaches for facility layout problems: The state-of-the-art and future research directions," European Journal of Operational Research, Elsevier, vol. 261(1), pages 1-16.
    3. Chaomin Luo & Miguel F. Anjos & Anthony Vannelli, 2008. "A nonlinear optimization methodology for VLSI fixed-outline floorplanning," Journal of Combinatorial Optimization, Springer, vol. 16(4), pages 378-401, November.
    4. Ignacio Castillo & Thaddeus Sim, 2004. "A spring-embedding approach for the facility layout problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 73-81, January.
    5. Miguel F. Anjos & Anthony Vannelli, 2006. "A New Mathematical-Programming Framework for Facility-Layout Design," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 111-118, February.
    6. Jankovits, Ibolya & Luo, Chaomin & Anjos, Miguel F. & Vannelli, Anthony, 2011. "A convex optimisation framework for the unequal-areas facility layout problem," European Journal of Operational Research, Elsevier, vol. 214(2), pages 199-215, October.

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