A Particle Swarm Optimal Algorithm for Multiple Path Toll Problems on Freeway Networks

In order to solve multiple path toll problems on freeway networks, firstly three evaluation indications are given for the multiple path toll methods. And a stochastic user equilibrium model is presented based on average OD travel time. Then, a particle swarm optimal algorithm is given, in the algorithm; two methods are used to deal with several constraints of the model. Finally, the numerical examples are given in a network. The results show the quality of method.