A solution to the road network design problem for multimodal flow

Given a set of candidate road projects associated with costs, finding the best subset with respect to a limited budget is known as the discrete network design problem (DNDP). The DNDP is often cast in a bilevel programming problem which is known to be NP-hard. Despite a plethora of research, due to the combinatorial complexity, efforts to address the problem for large-sized networks while considering public transport as well as other modes (multimodal/multiclass traffic flow) are scarce. To this end, we first turn the bilevel problem to a single-level problem based on System-Optimal traffic flow which results in a mixed integer non-linear programming (MINLP) problem. Second, we develop an efficient Benders decomposition algorithm to solve the ensuing MINLP problem. The multiclass/multimodal features of the traffic flow are ensured by employing the Spiess' bias term and optimal strategy methods. The proposed methodology is applied to Sioux Falls and a real sized network of the city of Winnipeg, Canada.