WardropN - Wardrop equilibrium ( Newton hybrid method )
Compute the Wardrop equilibrium of a transport assignment problem by solving the following nodes-links variational formulation of the problem:
Min_q Sum_l C(f_l)
f_l=Sum_i q_li
Hq_i=d_i
O<=q_li
where :
- C(f) is a cost in the classes defined by the lpf function, - H is is the incidence nodes-arcs matrix of the network, - q_li is the flow of the commodity i on the link l,
%net is the netlist containing all the information relative to the network and the cost function used.
The method used is a decomposed newton method in the space (q_i,v_i) i=1,p, where the v_i denote the dual variables associated to the constraints Hq_i=d_i .
The variable a regularizes the matrices giving the potentials. At each iteration a is reduced by a factor k. We can try first a small a and k=1.
This method is useful mainly in the case of a small number of commodities.
// Definition of the Network nw=4; %net=TrafficExample("Regular City",nw,nw); // Traffic Assignment bench=WardropN(0.1,2,1.e-4,12); // Visualization of the NET ShowNet();