Simulation-Based Optimization of Road Pricing in a Large Real-World Network

Simulation-Based Optimization of Road Pricing in a Large Real-World Network


Lei Zhang, University Of Maryland


This article develops a family of simulation/surrogate-based optimization approaches to approximate the response surface for the transportation simulation input–output mapping and search for the optimal toll charges in a transportation network.


This paper targets to optimize link-additive dynamic highway toll charging problem in a large transportation simulation network with expensive-to-evaluate objective using simulation-based optimization. In order to deal with the noise in simulation outputs, we will use quadratic polynomial RSM, Gaussian RBF, and regressing Kriging method, etc. (Jones, 1998; Jones et al., 2001; Fang and Horstemeyer, 2006; Kleijnen, 2009; Forrester and Keane, 2009) in this paper, to construct the surrogate models for an accurate prediction of the optimum of expensive-to-evaluate functions.

For the real large road network in the state of Maryland, an open source simulator DynusT (Dynamic Urban Systems in Transportation) is chosen as the dynamic traffic assignment (DTA) and mesoscopic vehicle simulation tool to evaluate network performance given various link-additive highway pricing rates. To search for the optimum price level to achieve minimum average travel time for all of the network users. The computation time needed to get a solution from conventional black-box function can be considerably reduced by the surrogate-based optimization models, several of which include global optima infill strategies make the noisy data processing and computation intensive global optimization feasible.

Building surrogate models is a very intuitive way in dealing with optimization problems with no-closed-form objective functions, especially when the evaluation of objective functions is very computationally expensive. This paper utilizes response surface models to solve the problem of minimizing average travel time by adjusting the variable toll rates of 5 links in a large real world road network: ICC network in Maryland. It shows that with only 97 samples, the infill Kriging model could already produce highly reliable estimates of simulation outputs over the entire feasible domain, and thus successfully help find out the optimal toll rate with minimized network average travel time. As the simulation of the ICC network costs about 50 to 60 minutes for each sample, the infill Kriging model helps reduce tremendous computation time compared to traditional scenario study, which needs to evaluate all possible solutions through the entire feasible domain.

The predicted optimal toll rate obtained from the infill Kriging model was then evaluated through simulation. The predicted output was relatively consistent with simulation outputs. The average travel time under optimal toll was 17.70 minutes, which is significantly shorter than the actual average travel time under current toll.

Future research will extend the simulation-based optimization methods to consider (1) Multiple objective functions; (2) Behavior adjustments: elastic demands; (3) Advanced exploitation of surrogates; and (4) Heterogeneous travelers: value of time distribution.


Association for European Transport