Development of the tree-based link labeling algorithm for optimal path-finding in urban transportation networks

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The optimal path-finding algorithm which is an important module in developing route guidance systems and traffic control systems has to provide correct paths to consider U-turns, P-turns, and no-left-turns in urban transportation networks. Traditional methods which have been used to consider those regulations on urban transportation networks can be categorized into network representation and algorithmic methods like the vine-building algorithm. First, network representation methods use traditional optimal path-finding algorithms with modifications to the network structure: for example, just adding dummy nodes and links to the existing network allows constraint-search in the network. This method which creates large networks is hard to implement and introduces considerable difficulties in network coding. With the increased number of nodes and links, the memory requirement tremendously increases, which causes the processing speed to slow down. For these reasons, the method has not been widely accepted for incorporating turning regulations in optimal path-finding problems in transportation networks. Second, algorithmic methods, as they are mainly based on the vine-building algorithm, have been suggested for determining optimal path for networks with turn penalties and prohibitions. However, the algorithms, although they nicely reflect the characteristics of urban transportation networks, frequently provide infeasible or suboptimal solutions. The algorithm to be suggested in this research is a method which is basically based on Dijkstra's algorithm [1] and the tree-building algorithm used to construct optimal paths. Unlike the traditional node labeling algorithms which label each node with minimum estimated cost, this algorithm labels each link with minimum estimated cost. Comparison with the vine-building algorithm shows that the solution of the link-labeling algorithm is better than that of the vine-building algorithm which very frequently provides suboptimal solutions. As a result, the algorithm allows turning regulations, while providing an optimal solution within a reasonable time limit.