On the minimization of traffic congestion in road networks with tolls

Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NP-hard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise-linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.