Using decomposition in large-scale highway network design with a Quasi-Optimization heuristic

The highway network design problem deals with the selection of links from a base network to facilitate the flow of vehicles from origins to destinations. A proper selection of links requires a balance between minimization of travel costs from origins to destinations and minimization of costs incurred in building or improving links in the network. Link construction costs are usually minimized as a part of the objective or constrained by budget availability. National or regional highway network design problems require excessive amounts of computing time, if solved to optimality. This paper presents a variation of the Modified Quasi-Optimization (MQO) heuristic developed by Dionne and Florian. The proposed algorithm solves a large network design problem by decomposing it in a sequence of smaller problems. Additional savings in computation time are achieved by limiting the search in the MQO heuristic to a well-designed set of paths for each OD pair. These paths are generated to suit the network design problem and differ from the K-shortest paths for the OD pairs. The combined use of decomposition and a limited set of paths allows the proposed heuristic to address realistic network design problems. Numerical experience with a problem involving 6563 nodes and 9800 two-ways links is reported.