### The Algorithm of the Time-Dependent Shortest Path Problem with Time Windows

Nasser A. El-Sherbeny
2014 Applied Mathematics
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 , the
more » ... , the timedependent shortest path problem with time windows asks to find an s, d-path that leaves a source node s at a departure time t 0 ; and minimizes the total arrival time at a destination node d. This formulation generalizes the classical shortest path problem in which c e are constants. Our algorithm of the time windows gave the generalization of the ALT algorithm and A * algorithm for the classical problem according to Goldberg and Harrelson [1], Dreyfus [2] and Hart et al. [3].