Variational Genetic Algorithm and Its Application to Urban Traffic Flow Control

Elena Sofronova


In dense urban road network, the influence of traffic lights at neighboring intersections becomes significant. Programs for switching the phases of traffic lights, which are called coordination plans, must agree. In the paper the problem of traffic flow control is considered as an optimal control problem. A universal recurrent traffic flow model based on the controlled networks theory is used. The mathematical model of the object is a system of recurrent finite-difference equations, which most closely corresponds to the system of differential equations applied in the optimal control theory. The proposed model allows to combine intersections, providing network extensibility. It is assumed that information about the state of the road network, maneuver parameters, input flows, restrictions on the capacity of vehicles on road sections and on the duration of traffic light phases, as well as the initial state of the traffic flow are known. It is necessary to find a control in the form of durations of phases of traffic lights at regulated intersections, taking into account the minimization of a given quality criterion. The solution of the problem is the optimal coordination plan for all regulated intersections of the network in a specific period of time. The optimal control problem of traffic flows is stated and a method for solving it by variational genetic algorithm is presented. The method uses the principle of small variations of the basic solution. According to this principle, one basic solution, the current coordination plan, is given and all other possible solutions are determined by the set of codes of small variations of the basic solution. A description of the variational genetic algorithm is provided. Examples of variations of the basic solution and the execution of basic genetic operations on them are presented. The proposed method is used to solve the optimal control problem for a group of traffic lights in the Northern Administrative District of Moscow.

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