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Approximate Solutions of Continuous Dispersion Problems

Author

Listed:
  • Artan Dimnaku
  • Rex Kincaid
  • Michael Trosset

Abstract

The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the maximin distance design problem). This problem can be formulated as a nonlinear program, either exactly or approximately. We consider formulations of both types and demonstrate that, as p increases, it becomes dramatically more expensive to compute solutions of the exact formulation than to compute solutions of the approximate formulation. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Artan Dimnaku & Rex Kincaid & Michael Trosset, 2005. "Approximate Solutions of Continuous Dispersion Problems," Annals of Operations Research, Springer, vol. 136(1), pages 65-80, April.
    • Handle: RePEc:spr:annopr:v:136:y:2005:i:1:p:65-80:10.1007/s10479-005-2039-z
    DOI: 10.1007/s10479-005-2039-z
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    Cited by:

    1. B. Addis & M. Locatelli & F. Schoen, 2008. "Disk Packing in a Square: A New Global Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 516-524, November.
    2. Edwin R. van Dam & Bart Husslage & Dick den Hertog & Hans Melissen, 2007. "Maximin Latin Hypercube Designs in Two Dimensions," Operations Research, INFORMS, vol. 55(1), pages 158-169, February.
    3. Husslage, B.G.M. & Rennen, G. & van Dam, E.R. & den Hertog, D., 2008. "Space-Filling Latin Hypercube Designs For Computer Experiments (Revision of CentER DP 2006-18)," Other publications TiSEM 1b5d18c7-b66f-4a9f-838c-b, Tilburg University, School of Economics and Management.
    4. Husslage, B.G.M. & Rennen, G. & van Dam, E.R. & den Hertog, D., 2008. "Space-Filling Latin Hypercube Designs For Computer Experiments (Revision of CentER DP 2006-18)," Discussion Paper 2008-104, Tilburg University, Center for Economic Research.
    5. Zhengguan Dai & Kathleen Xu & Melkior Ornik, 2021. "Repulsion-based p-dispersion with distance constraints in non-convex polygons," Annals of Operations Research, Springer, vol. 307(1), pages 75-91, December.
    6. Xiangjing Lai & Jin-Kao Hao & Renbin Xiao & Fred Glover, 2023. "Perturbation-Based Thresholding Search for Packing Equal Circles and Spheres," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 725-746, July.

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