Bilevel programming for the continuous transport network design problem

A Continuous Network Design Problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. A bilevel programming technique can be used to formulate this equilibrium network design problem. At the upper level problem, the system performance index is defined as the sum of total travel times and investment costs of link capacity expansions. At the lower level problem, the user equilibrium flow is determined by Wardrop's first principle and can be formulated as an equivalent minimization problem. In this paper we exploit a descent approach via the implementation of gradient-based methods to solve CNDP generally where the Karush-Kuhn-Tucker points can be obtained. Four variants of gradient-based methods are presented and numerical comparisons are widely made with the previous on three kinds of test networks. The proposed methods have achieved substantially better results in terms of the robustness to the initials and the computational efficiency in solving equilibrium assignment problems than did others especially when the congested road networks are considered.