Curvature-constrained Steiner networks with three terminals

Peter A. Grossman (), David Kirszenblat (), Marcus Brazil (), J. Hyam Rubinstein () and Doreen A. Thomas ()
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Peter A. Grossman: The University of Melbourne
David Kirszenblat: The University of Melbourne
Marcus Brazil: The University of Melbourne
J. Hyam Rubinstein: The University of Melbourne
Doreen A. Thomas: The University of Melbourne

Journal of Global Optimization, 2024, vol. 90, issue 3, No 6, 710 pages

Abstract: 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.

Keywords: Steiner network; Curvature constraint; Underground mine design; Dubins path (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01414-z

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