Improvements of the Traffic Signal Control by Complex-Valued Hopfield Networks

The phase synchronization in the complex-valued Hopfield network has been shown to be effective for a signal control in an area-wide urban traffic flow control. The basic idea of the original method is to attain the global effectiveness as a weighted summation of the local effectiveness. And the complex-valued Hopfield network is designed to converge to such an optimal state through the appropriate interaction between the neurons which model the traffic signals. As the result, the network possesses the energy function which expresses the global effectiveness, whose leading term is given by the summation of the substantial traffic flows under the given offset. Thus, it is a bottom-up approach to optimize the global effectiveness as the total of the local effectiveness. In this paper, two different approaches are introduced, and added to or compared with the above approach. The first approach is the feedback from the real time information of local traffics. The purpose of the feedback is to decrease the differences of the disadvantages among conflicting flows, which are measured by a congestion or the number of waiting vehicles. The addition of the feedback to the original method shows that the local feedback works as a pinpoint control on a local congestion, while keeping the total effectiveness especially in regular traffic patterns. The second is a top-down approach to attain the global optimization by real-coded genetic algorithms. The proposed GA directly searches the effective offset using a traffic simulator to calculate the average traveling time for the evaluation. Therefore, genetic operations are designed for a small size population and a real-code in a torus space. The best offsets obtained by GA reduce the average traveling time by 2%~7% compared with the results obtained by the original approach.