Multi-objective optimization of traffic externalities using tolls

Genetic algorithms (GAs) are widely accepted by researchers as a method of solving multi-objective optimization problems (MOPs), at least for listing a high quality approximation of the Pareto front of a MOP. In traffic management, it has been long established that tolls can be used to optimally distribute traffic in a network with aim of combating some traffic externalities such as congestion, emission, noise, safety issues. Formulating the multi-objective toll problem as a one point solution problem fails to give the general overview of the objective space of the MOP. Therefore, in this paper we develop a game theoretic approach that gives the general overview of the objective space of the multiobjective problem and compare the results with those of the wellknown genetic algorithm non-dominated sorting genetic algorithm II (NSGA-II). Results show that the game theoretic approach presents a promising tool for solving multi-objective problems, since it produces similar non-dominated solutions as NSGA-II, indicating that competing objectives (or stakeholders in the game setting) can still produce Pareto optimal solutions. Most fascinating is that a range of non-dominated solutions is generated during the game, and almost all generated solutions are in the neighborhood of the Pareto set. This indicates that good solutions are generated very fast during the game.