Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks

Authors Matúš Mihalák, Sandro Montanari

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Matúš Mihalák
Sandro Montanari

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Matúš Mihalák and Sandro Montanari. Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 82-94, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Based on time-dependent travel times for N past days, we consider the computation of robust routes according to the min-max relative regret criterion. For this method we seek a path minimizing its maximum weight in any one of the N days, normalized by the weight of an optimum for the respective day. In order to speed-up this computationally demanding approach, we observe that its output belongs to the Pareto front of the network with time-dependent multi-criteria edge weights. We adapt a well-known algorithm for computing Pareto fronts in time-dependent graphs and apply the bi-directional search technique to it. We also show how to parametrize this algorithm by a value K to compute a K-approximate Pareto front. An experimental evaluation for the cases N = 2 and N = 3 indicates a considerable speed-up of the bi-directional search over the uni-directional.
  • shortest path
  • time-dependent
  • bi-criteria
  • bi-directional search
  • min-max relative regret


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