Exact local solution of the continuous network design problem via stochastic user equilibrium assignment

The continuous Network Design Problem (NDP) deals with determining optimal expansions for the capacities of a street network, subject to the constraint that the street traffic volumes must be the outcome of a user-optimal equilibrium assignment. Although the use of deterministic equilibrium methods tends to produce computationally intractable problems, in this paper it is shown that a stochastic user equilibrium based on the logit model leads to a differentiable and large-scale, but tractable, version of the NDP. A procedure for computing the derivatives of the stochastic user equilibrium (SUE) assignment without having to first compute the route choice probabilities is given, and this procedure is coupled with two standard algorithms for solving nonlinear programs, the generalized reduced gradient method and sequential quadratic programming. These algorithms are tested on several example networks, and the results of these tests suggest that the SUE-constrained version of the NDP offers both a promising heuristic for solving DUE-constrained problems as well as a viable procedure in its own right.