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In this paper, we present a new algorithm of the time-dependent shortest path problem with time windows. Give a directed graph ( ) , G V E = , where V is a set of nodes, E is a set of edges with a non-negative transit-time function ( ) e c t . For each node v V ∈ , a time window [ ] , v v a b within which the node may be visited and v v a t b ≤ ≤ , t T ∈ is non-negative of the service and leaving time of the node. A source node s, a destination node d and a departure time t 0 , thedoi:10.4236/am.2014.517264 fatcat:7rwyd662tzcqxnm34m77bh7gwu