A New Discrete Traffic Network Design Problem with Evolutionary Game Algorithm

Abstract

The discrete network design problem deals with the selection of link additions to an existing road network, with given demand from each origin to each destination. The objective is to make an optimal investment decision in order to minimize the total travel cost in the network, while accounting for the route choice behaviors of network users. The discrete network design problem is considered as a two-stage Stackelberg game and is formulated as a combinatorial bi-level programming problem. The traditional lower-level model is user equilibrium based on path flow. The key to solve the lower-level model is to enumerate all the paths between each pair of origin and destination, which is difficult to a large-scale complex network. So in this paper, at first a traditional bi-level programming model for the discrete network design problem is introduced, and then a new bi-level programming model is proposed, in which the lower-level model is based on link flow. Then a new algorithm for upper-level problem is proposed by using evolutionary game algorithm (EGA), and the lower-level by Frank-Wolfe Algorithm. Finally, the applications of the new algorithm are illustrated with a numerical example. The numerical results show that the algorithm is feasible and effective.