A Physarum-inspired Model for the Probit-based Stochastic User Equilibrium Problem
Shuai Xu, Wen Jiang and Xin Li
Stochastic user equilibrium is an important issue in the traffic assignment problems, traditional models for the stochastic user equilibrium problem are designed as mathematical programming problems. A Physarum-inspired model for the probit-based stochastic user equilibrium problem is proposed. There are two main contributions of our work. On the one hand, the original Physarum model is modified to find the shortest path in directed traffic 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 a two-step procedure. First, the modified Physarum model is applied to estimate the auxiliary flows. Second, the auxiliary flows are averaged to obtain the equilibrium flows. Numerical examples are analysed to evaluate the performance of the proposed method, which is compared with the Method of Successive Average method.
Keywords: Networks, optimisation algorithms, physarum, stochastic, traffic equilibrium