Notes on using simulation-optimization techniques in traffic simulation

Abstract

Mathematical and simulation models of systems lay at the core of many decision support systems, and their role becomes more critical when the system is more complex. The decision process usually involves optimizing some utility function that evaluates the performance indicators measuring the impacts of the decisions. The complexity of the system directly increases the difficulty when the associated function to be optimized is a non-analytical, non-differentiable, non-linear function that can only be evaluated by simulation. Simulation-optimization techniques are especially suited to these cases, and its use is becoming increasingly used with traffic models, which represent an archetypal case of complex, dynamic systems that exhibit highly stochastic characteristics. In this approach, simulation is used to evaluate the objective function, and it is combined with a non-differentiable optimization technique for solving the associated optimization problem. Of these techniques, one of the most commonly used is Stochastic Perturbation Stochastic Approximation (SPSA).

This paper analyses, discusses and presents the computational results from applying this technique in the calibration of traffic simulation models. This study uses variants of the SPSA by replacing the usual gradient approach with a combination of projected gradient and trust region methods. A special approach has also been analyzed for parameter calibration cases in which each variable has a different magnitude.