A user-optimal model for route planning problem

In this paper, a user-optimal mode is proposed, which takes into account the user equilibrium for initial route planning in the plain area and the effect of lake located nearby the Central Business District (CBD) on flow intensity. We consider a city with two highly compact CBDs and a lake. Within the city region, commuters are assumed to be scattered continuously over the city and each commuter is assumed to choose a CBD to minimize individual total cost. The total cost depends on the location, the traffic flow intensity and a cost associated with the congestion externality at the CBD. Furthermore, the traffic demand from any destination in the city to the CBD is assumed to be a function of both the destination location and the total travel cost to the CBD. The model is formulated as a calculus of variations problem. Then finite element method and evolutionary structural optimization (ESO) is used to solve and optimize the model. Finally we find the initial location of future artery through solving the continuum user equilibrium problem. Numerical experiment shows the effectiveness of the proposed methodology.