Un estudio de la implementación del método del conjunto activo en procedimientos de asignación de redes de tráfico

Resumo

The active set method is one of the most extended methods for optimization of non-linear functions subject to linear restrictions. The formulation of the principle of user equilibrium in networks according to the principle of Wardrop was withdrawal by Beckman, McGuire and Winsten in 1956, and whose customary resolution method is accomplished through the employment of the convex combinations algorithm by Frank-Wolfe. We propose the application of the active set method to this type of formulation using a cost function type BPR. The results show the best degree of convergence and the better developments that are obtained through this method as compared to Frank-Wolfe. We consider the application of the method to networks with asymmetric interaction effects through a diagonalization algorithm with good results. We present an estimate of the optimum toll as function of the differences between the public marginal cost and the private marginal cost, such as the objective function of the user equilibrium assignment results smaller than the traditional optimum toll that is based on the difference between marginal cost and short term medium cost, employing as resolution the active set method. We implement the active set method in computer using the program of symbolic calculus Mathematica; in order to provide some examples of traffic assignment in networks.