Bidirectional dynamic programming is an algorithm that searches for paths in a network from both the starting and the ending nodes that optimize a given objective function. In recent years, bidirectional dynamic programming has been shown to be an effective means for solving resource-bounded shortest path problems. While many researchers have observed that bidirectional A ⋆ approaches perform poor computationally, we exploit the presence of resource constraints to overcome the source of these computational challenges. Our main contribution in this paper is an exact bidirectional A ⋆ algorithm for resource-constrained shortest path problems (RCSPPs) that is capable of solving large-sized instances that challenge the state-of-the-art in the literature. We also analyze, both computationally and theoretically, the sensitivity of the algorithm's performance to its inputs.
Given a graph whose arc traversal times vary over time, the Time‐Dependent Travelling Salesman Problem consists of finding a Hamiltonian tour of least total duration. In this paper we exploit some properties of the problem and develop a branch‐and‐bound algorithm which outperforms the state‐of‐the‐art branch‐and‐cut procedure by Cordeau et al. [5].
The fast computation of point-to-point quickest paths on very large time-dependent road networks will allow next-generation web-based travel information services to take into account both congestion patterns and realtime traffic informations. The contribution of this article is threefold. First, we prove that, under special conditions, the Time-Dependent-Quickest Path Problem (QPP) can be solved as a static QPP with suitable-defined (constant) travel times. Second, we show that, if these special conditions do not hold, the static quickest path provides a heuristic solution for the original time-dependent problem with a worst-case guarantee. Third, we develop a time-dependent lower bound on the time-to-target which is both accurate and fast to compute. We show the potential of this bound by embedding it into a unidirectional A * algorithm which is tested on large metropolitan graphs. Computational results show that the new lower bound allows to reduce the computing time by 27% on average.
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