Abstract
Vehicle traffic remains a major source of air pollutants that affect human health and contribute to anthropogenic climate change. These negative externalities can be reduced, in part, with the implementation of environmentally-oriented road pricing schemes. In this paper a toll design problem (TDP) is proposed for determining toll locations and levels that minimize the expected human intake of air pollutants subject to constraints on pollutant concentration levels and implementation costs. The application of the proposed problem is hindered by the computational costs associated with the evaluation of candidate solutions, as is common for network design problems (NDPs). Furthermore, given that multiple types of models (e.g., traffic assignment, emissions, and air dispersion models) would be required to evaluate a design alternative, in practice the proposed TDP could result in a black-box optimization problem. Consequently, a derivative-free surrogate-based solution algorithm is proposed for the mixed integer TDP. A numerical example is utilized to illustrate a possible application of the proposed model and test the performance of the surrogate-based algorithm. Relative to a joint simulated annealing-genetic algorithm heuristic and a genetic algorithm-based approach, the proposed algorithm found better solutions in notably fewer model function evaluations.