Physarum polycephalum assignment: a new attempt for fuzzy user equilibrium

The fuzzy user equilibrium problem in urban traffic assignment has attracted much attention since its great theoretical significance and wide application. Based on the fact that travelers tend to choose the minimum-cost path between every origin–destination pair of the traffic network, an equilibrium is emerging over time. However, in the real world, travelers’ selection of paths is often fuzzy with the lack of global information. In this paper, by aid of the Physarum polycephalum algorithm, we propose a model for solving the fuzzy user equilibrium problem. P. polycephalum can build a bio-network and assign the flow according to the location and the size of the food source. Taking full advantage of this feature, the proposed model associates the traffic demand with the food source and unifies the bio-network and the traffic network. The solution of the fuzzy user equilibrium problem is the flow assignment in the bio-network. To test the performance of the proposed method, we conduct experiments on some traffic networks selected from recent related works. The results show that the proposed method is efficient.