Cone projection versus half-space projection for the bilevel optimisation of transportation networks

This paper describes the half-space projection method and cone-projection method of optimising an urban transportation model. The paper then compares these two methods as applied to seek optimal capacity changes within a very simple example network model. The optimisation has, in each of the cases, a bilevel character since it is performed on two functions; the equilibrium function E (which must have value zero for equilibrium) and the objective function Z which is minimised subject to the constraint that E is zero. Thus E = 0 (or ‘small’) always has priority.