Shortest Paths with Shortest Detours

Carolin Torchiani (), Jan Ohst (), David Willems () and Stefan Ruzika ()
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Carolin Torchiani: Universität Koblenz-Landau
Jan Ohst: Universität Koblenz-Landau
David Willems: Universität Koblenz-Landau
Stefan Ruzika: Universität Koblenz-Landau

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 14, 858-874

Abstract: Abstract This paper is concerned with a biobjective routing problem, called the shortest path with shortest detour problem, in which the length of a route is minimized as one criterion and, as second, the maximal length of a detour route if the chosen route is blocked is minimized. Furthermore, the relation to robust optimization is pointed out, and we present a new polynomial time algorithm, which computes a minimal complete set of efficient paths for the shortest path with shortest detour problem. Moreover, we show that the number of nondominated points is bounded by the number of arcs in the graph.

Keywords: Networks; Shortest paths; Biobjective programming; Detours; Recovery robustness; 90C27; 90C29; 90C35 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1145-9

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