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A global optimization procedure for the location of a median line in the three-dimensional space

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  • Blanquero, Rafael
  • Carrizosa, Emilio
  • Schöbel, Anita
  • Scholz, Daniel

Abstract

A global optimization procedure is proposed to find a line in the Euclidean three-dimensional space which minimizes the sum of distances to a given finite set of three-dimensional data points. Although we are using similar techniques as for location problems in two dimensions, it is shown that the problem becomes much harder to solve. However, a problem parameterization as well as lower bounds are suggested whereby we succeeded in solving medium-size instances in a reasonable amount of computing time.

Suggested Citation

  • Blanquero, Rafael & Carrizosa, Emilio & Schöbel, Anita & Scholz, Daniel, 2011. "A global optimization procedure for the location of a median line in the three-dimensional space," European Journal of Operational Research, Elsevier, vol. 215(1), pages 14-20, November.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:1:p:14-20
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    Cited by:

    1. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.

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