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arXiv:2403.18363v1 Announce Type: new
Abstract: The safety of streets is difficult to quantify numerically. However, it is possible to sort streets regarding their safety into ordered categories, like safe, neutral and unsafe. In this paper we model the computation of safe bicycle routes as an optimization problem with ordinal coefficients. We describe an appropriate optimality concept for ordinal optimization problems and introduce a solution strategy for ordinal routing problems. Furthermore, we introduce a concept to incorporate safety preferences by introducing weights such that longer path with a higher safety rating are preferred. We apply the concept of ordinal routing to compute safe bicycle routes in Stuttgart, Germany, based on dates from OpenStreetMaps. We show that the choice of the weights does not only represent the trade-off of safety vs. path length, but has also an impact on the number of alternative solutions and thus on the computation time.
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Die Sicherheit von Wegen ist nur eingeschr\"ankt messbar und daher schwierig zu quantifizieren. Dahingegen ist es verh\"altnism\"a{\ss}ig leicht Wege bez\"uglich ihrer Sicherheit in geordnete Kategorien, wie beispielsweise sicher, neutral und gef\"ahrlich einzuordnen. In diesem Beitrag werden Optimierungsprobleme mit geordneten Kategorien formuliert und Optimalit\"at f\"ur diese definiert. Daraus wird eine L\"osungsstrategie f\"ur solche Probleme abgeleitet. Dar\"uber hinaus wird erkl\"art, wie die Abgrenzung zwischen den Kategorien erh\"oht werden kann, sodass l\"angere aber daf\"ur sicherere Wege mit Hilfe von Gewichten berechnet werden k\"onnen. Diese theoretischen Ergebnisse werden in der Praxis angewendet und es werden auf Grundlage von Daten von OpenStreetMaps sichere Fahrradwege in Stuttgart berechnet. Dabei zeigt sich, dass eine gute Wahl der Gewichte zu weniger L\"osungen und k\"urzeren Rechenzeiten f\"uhrt.

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