Optimizing Frequencies in a Transit Network: a Nonlinear Bi-level Programming Approach

We consider the problem of optimizing the frequencies of transit lines in an urban transportation network. The problem is formulated first as a nonlinear nonconvex mixed integer programming problem and then it is converted into a bi-level Min–Min nonconvex optimization problem. This problem is solved by a projected (sub)gradient algorithm, where a (sub)gradient is obtained at each iteration by solving the lower level problem. Computational results obtained with this algorithm are presented for the transit networks of the cities of Stockholm, Sweden, Winnipeg, Man., Canada and Portland, OR, U.S.A.