Accounting for population exposure to vehicle-generated pollutants and environmental equity in the toll design problem

The emissions generated by motor vehicles remain a major source of air pollutants that affect public health and contribute to anthropogenic climate change. These negative externalities can be reduced, in part, with the implementation of environmentally oriented road pricing schemes, which can be designed using optimization-based approaches. In this paper, a toll design problem is proposed for determining toll locations and levels that minimize the expected human exposure to air pollutants and the related environmental inequalities, subject to constraints on pollutant concentration levels and implementation costs. The practical use of the proposed problem is hindered in most real-world applications by the computational costs associated with the evaluation of candidate solutions, as is common for network design problems. Furthermore, the problem cannot be expressed analytically given the multiple types of models (e.g., traffic assignment, emissions, air dispersion models) that would be required to evaluate a single design alternative. For these reasons, a derivative-free surrogate-based solution algorithm is proposed for mixed integer problems like the ones considered here. Numerical examples are used to illustrate possible applications of the proposed model and to 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 fewer function evaluations.