An energy-efficient reliable path finding algorithm for stochastic road networks with electric vehicles

In this paper, we develop a novel reliable path finding algorithm for a stochastic road network with uncertainty in travel times while both electric vehicle energy and efficiency are simultaneously taken into account. We first propose a bi-objective optimization model to maximize (1) the on-time arrival reliability and (2) energy-efficiency for battery electric vehicles (BEVs) in a path finding problem. The former objective requires finding the reliable shortest path (RSP), which is the path with the minimal effective travel time measured by the sum of the mean travel time and a travel time safety margin for any given origin-destination (OD) pair. Then, we refer to energy-efficiency as the minimum of the electric energy consumption. We discuss the non-additive property of the RSP problem since we also consider the link travel time correlations, whereas the latter objective satisfies the additive criterion. To this end, we illustrate the existence of non-dominated solutions that satisfy both of the two objectives. Furthermore, it is shown that the intersection of two candidate sets - one for the RSPs and the other for paths with minimal energy-consumption - actually contains the optimal solution for the bi-objective optimization problem. The upper and lower bounds of the effective travel time are mathematically deduced and can be used to generate the candidate path set of this bi-objective problem via the K-shortest algorithm. Our proposed algorithm overcomes the infeasibility of traditional path finding algorithms (e.g., the Dijkstra algorithm) for RSPs. Moreover, using two numerical examples, we verify the effectiveness and efficiency of the proposed algorithm. We numerically demonstrate promising potential applications of the proposed algorithm in real-life road traffic networks.