One of the main functions of the traffic navigation systems is to find the optimal route to the destination. In this paper, we propose an iterative Q value updating algorithm, Q method, based on dynamic programming to search the optimal route and its optimal traveling time for a given Origin-Destination (OD) pair of road networks. The Q method uses the traveling time information available at adjacent intersections to search for the optimal route. The Q value is defined as the minimum traveling time to the destination when a vehicle takes the next intersection. When the Q values converge, the optimal route to the destination can be determined by choosing the minimum Q value at each intersection. The Q method gives us the solutions from multiple origins to a single destination. The proposed method is not restricted to find a single solution, but, if there exist multiple optimal routes with the identical traveling time to the destination, the proposed method can find all of it. In addition to that, when the traveling time of the road sections changes, an alternative optimal route can be found easily starting with the already obtained Q values. We compared the Q method with Dijkstra algorithm and the simulation results showed that the Q method can give better performances, depending on the situations, when the traveling time of the road sections changes.

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Optimal route search to the destination is one of the most important functions of car navigation devices. The development of road traffic infrastructure has made it possible to receive real-time information of the traffic situation. Route search algorithms for car navigation devices make use of this information to avoid the traffic congestions. Such algorithms should find the new optimal route efficiently when the traffic situation changes. Usually, the minimum traveling time or distance is considered to define the optimal route. However, the minimum traveling time or distance is not always what the user is looking for. The user may prefer to travel on a certain route even at the cost of traveling time or distance. Car navigation devices should consider such preferences when finding the optimal route. In this paper, we propose a dynamic programming algorithm to find the optimal route considering that it should deal with the changes of the traffic situation and multiple criteria. The proposed method uses the information from the previous computation to find the new optimal route considering user preferences when the traveling time of the road section changes. The proposed method was applied to a real road network to find the optimal route. Results show that the proposed method can find the user-preferred optimal route. Simulation results also show better calculation time of the proposed method compared to the Dijkstra algorithm. 

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