A Physarum-inspired Model for the Probit-based Stochastic User Equilibrium Problem

Stochastic user equilibrium is an important issue in the traffic assignment problems, tradition models for the stochastic user equilibrium problem are designed as mathematical programming problems. In this article, a Physaruminspired model for the probit-based stochastic user equilibrium problem is proposed. There are two main contributions of our work. On the one hand, the origin Physarum model is modified to find the shortest path in traffic direction networks with the properties of two-way traffic characteristic. On the other hand, the modified Physarum-inspired model could get the equilibrium flows when traveller’s perceived transportation cost complies with normal distribution. The proposed method is constituted with a two-step procedure. First, the modified Physarum model is applied to get the auxiliary flows. Second, the auxiliary flows are averaged to obtain the equilibrium flows. Numerical examples are conducted to illustrate the performance of the proposed method, which is compared with the Method of Successive Average method.