Optimising Differentiated Tolls on Large Scale Networks, by Using an Intelligent Search Algorithm

Optimising Differentiated Tolls on Large Scale Networks, by Using an Intelligent Search Algorithm


T Brands, D H van Amelsfort, Goudappel Coffeng, NL


A framework to optimise space and time differentiated link tolls with respect to a specific objective is presented and applied on real cases. A pattern search algorithm is executed, using a constrained solution space for computational feasibility.


Differentiated road pricing schemes are defined by different design dimensions, such as a price level for each road section, for each time, and for different road users. Different policy objectives lead to different optimal designs of schemes. The problem is to find the optimal price levels to meet the policy objectives, which are mathematically formulated in an objective function. The price levels can however not be varied freely, as public acceptance, user understanding of the system, etc. impose social constraints. Many studies solved this optimisation problem in a theoretical setting. In larger and more realistic networks however, the optimisation problem is still computationally infeasible, because the solution space is immense and each model evaluation is time consuming. This research presents a method of optimising toll levels in realistic networks using an intelligent search algorithm combined with an approach to limit the solution space.

To reduce the solution space, reference run analyses (without tolls) are used to determine levels of aggregation in time and in space. When similarities (e.g. link characteristics, flows) between links are large, links are grouped together and equal tolls are imposed. In addition to this, the modelled time period (e.g. peak period) is divided in a limited number of logical time intervals. For a peak period, the course of the dynamic tolls (height and shape) is partly predetermined, based on the demand profile or on congestion levels in the reference run. After applying constraints to the solution space, an initial solution is determined, where link groups and time periods which contribute most negatively to the objective function value, get the maximum toll value, whereas quiet periods and link groups get the minimum level.

A pattern search algorithm is then executed to improve the initial solution, within the defined constraints. In the paper we discuss different pattern search algorithms and different objective functions (policy objectives). Furthermore, other methods like grid search and genetic algorithms are compared in a qualitative analysis.

To test the optimisation approach a modelling framework is used that includes a departure time choice model to determine the effects of changes in dynamic travel costs and travel times. The effects of these changes on route choice and the resulting network flows are determined using a macroscopic dynamic traffic assignment model with multiple user classes. The level of demand may change using an elastic demand approach.

The optimisation framework is tested on two real cases in the Netherlands: a rough network of the town of Delft and a more detailed network of the city of The Hague and the two surrounding towns of Zoetermeer and Delft. These area?s are all in the western part of the Netherlands and they include several major motorways. For the Delft network a solution with 15% less congestion than a logical predefined toll setting has been found. With regard to the situation without road pricing the congestion has been reduced by 41%. Similar results are found for the larger and more detailed The Hague network, but need to be further researched. New results will be included in the final paper.


Association for European Transport