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Fitting concentric circles to measurements

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  • Zvi Drezner
  • Jack Brimberg

Abstract

Measurements for fitting a given number of concentric circles are recorded. For each concentric circle several measurements are taken. The problem is to fit the given number of circles to the data such that all circles have a common center. This is a generalization of the problem of fitting a set of points to one circle. Three objectives, to be minimized, are considered: the least squares of distances from the circles, the maximum distance from the circles, and the sum of the distances from the circles. Very efficient optimal solution procedures are constructed. Problems based on a total of 10,000 measurements are solved in about 10 s with the least squares objective, $$>$$ > 2 s with the maximum distance objective, and a little more than 1 min for the minisum objective. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Zvi Drezner & Jack Brimberg, 2014. "Fitting concentric circles to measurements," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 119-133, February.
    • Handle: RePEc:spr:mathme:v:79:y:2014:i:1:p:119-133
    DOI: 10.1007/s00186-013-0455-4
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    References listed on IDEAS

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    1. Tammy Drezner & Zvi Drezner, 2007. "Equity Models in Planar Location," Computational Management Science, Springer, vol. 4(1), pages 1-16, January.
    2. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    3. Labbe, Martine & Laporte, Gilbert & Rodriguez Martin, Inmaculada & Gonzalez, Juan Jose Salazar, 2005. "Locating median cycles in networks," European Journal of Operational Research, Elsevier, vol. 160(2), pages 457-470, January.
    4. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    5. C. E. M. Pearce, 1974. "Locating Concentric Ring Roads in a City," Transportation Science, INFORMS, vol. 8(2), pages 142-168, May.
    6. Chernov, N. & Sapirstein, P.N., 2008. "Fitting circles to data with correlated noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5328-5337, August.
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    Cited by:

    1. Loay Alkhalifa & Jack Brimberg, 2017. "Locating a minisum annulus: a new partial coverage distance model," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 373-393, July.

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