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A fast Voronoi-diagram algorithm with applications to geographical optimization problems

  • Non-Linear Programming, Algorithms
  • Conference paper
  • First Online:
System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 59))

Abstract

There are many kinds of facility location problems, or "geographical optimization problems", which are appropriately formulated in terms of the Voronoi diagram. Except few quite special problems, we can get a solution to a problem of that kind only by means of numerical approach which involves a large number of function evaluations, where each evaluation requires constructing the Voronoi diagram for a tentative distribution of facilities and computing integrals with reference to that diagram. In such a case, the practical feasibility of the numerical solution of the problem depends largely upon the efficiency of the algorithm to be used for constructing the Voronoi diagram. In this paper, we shall formulate a class of location problems and show that, if we use the Voronoi-diagram algorithm recently proposed by the authors, we can numerically solve considerably large problems within a practicable time.

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Author information

Authors and Affiliations

  1. University of Tokyo, Tokyo, Japan

    Masao Iri

  2. University of Tsukuba, Ibaraki, Japan

    Kazuo Murota

  3. Central Research Institute of Electric Power Industry, Tokyo, Japan

    Takao Ohya

Authors
  1. Masao Iri
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  2. Kazuo Murota
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  3. Takao Ohya
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Editor information

P. Thoft-Christensen

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© 1984 Springer-Verlag

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Iri, M., Murota, K., Ohya, T. (1984). A fast Voronoi-diagram algorithm with applications to geographical optimization problems. In: Thoft-Christensen, P. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008901

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  • DOI: https://doi.org/10.1007/BFb0008901

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13185-4

  • Online ISBN: 978-3-540-38828-9

  • eBook Packages: Springer Book Archive

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