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Curvature-constrained Steiner networks with three terminals

Author

Listed:
  • Peter A. Grossman

    (The University of Melbourne)

  • David Kirszenblat

    (The University of Melbourne)

  • Marcus Brazil

    (The University of Melbourne
    ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA))

  • J. Hyam Rubinstein

    (The University of Melbourne)

  • Doreen A. Thomas

    (The University of Melbourne
    ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA))

Abstract

A procedure is presented for finding the shortest network connecting three given undirected points, subject to a curvature constraint on both the path joining two of the points and the path that connects to the third point. The problem is a generalisation of the Fermat–Torricelli problem and is related to a shortest curvature-constrained path problem that was solved by Dubins. The procedure has the potential to be applied to the optimal design of decline networks in underground mines.

Suggested Citation

  • Peter A. Grossman & David Kirszenblat & Marcus Brazil & J. Hyam Rubinstein & Doreen A. Thomas, 2024. "Curvature-constrained Steiner networks with three terminals," Journal of Global Optimization, Springer, vol. 90(3), pages 691-710, November.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:3:d:10.1007_s10898-024-01414-z
    DOI: 10.1007/s10898-024-01414-z
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    References listed on IDEAS

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    1. D. Kirszenblat & K. G. Sirinanda & M. Brazil & P. A. Grossman & J. H. Rubinstein & D. A. Thomas, 2018. "Minimal curvature-constrained networks," Journal of Global Optimization, Springer, vol. 72(1), pages 71-87, September.
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