SIMULATION-BASED OPTIMIZATION OF TRANSPORTATION SYSTEMS: THEORY, SURROGATE MODELS, AND APPLICATIONS
Abstract
The construction of new highway infrastructure has not kept pace with the growth of travel, mainly due to the limitation of land and funding availability. To improve the mobility, safety, reliability and sustainability of the transportation system, various transportation planning and traffic operations policies have been developed in the past few decades. On the other hand, simulation is widely used to evaluate the impacts of those policies, due to its advantages in capturing network and behavior details and capability of analyzing various combinations of policies. A simulation-based optimization (SBO) method, which combines the strength of simulation evaluation and mathematical optimization, is imperative for supporting decision making in practice.
The objective of this dissertation is to develop SBO methods that can be efficiently applied to transportation planning and operations problems. Surrogate-based methods are selected as the research focus after reviewing various existing SBO methods. A systematic framework for applying the surrogate-based optimization methods in transportation research is then developed. The performance of different forms of surrogate models is compared through a numerical example, and regressing Kriging is identified as the best model in approximating the unknown response surface when no information regarding the simulation noise is available. Accompanied with an expected improvement global infill strategy, regressing Kriging is successfully applied in a real world application of optimizing the dynamic pricing for a toll road in the Inter-County Connector (ICC) regional network in the State of Maryland. To further explore its capability in dealing with problems that are of more interest to planners and operators of the transportation system, this method is then extended to solve constrained and multi-objective optimization problems.
Due to the observation of heteroscedasticity in transportation simulation outputs, two surrogate models that can be adapted for heteroscedastic data are developed: a heteroscedastic support vector regression (SVR) model and a Bayesian stochastic Kriging model. These two models deal with the heteroscedasticity in simulation noise in different ways, and their superiority in approximating the response surface of simulations with heteroscedastic noise over regressing Kriging is verified through both numerical studies and real world applications. Furthermore, a distribution-based SVR model which takes into account the statistical distribution of simulation noise is developed. By utilizing the bootstrapping method, a global search scheme can be incorporated into this model. The value of taking into account the statistical distribution of simulation noise in improving the convergence rate for optimization is then verified through numerical examples and a real world application of integrated corridor traffic management.
This research is one of the first to introduce simulation-based optimization methods into large-scale transportation network research. Various types of practical problems (with single-objective, with multi-objective or with complex constraints) can be resolved. Meanwhile, the developed optimization methods are general and can be applied to analyze all types of policies using any simulator. Methodological improvements to the surrogate models are made to take into account the statistical characteristics of simulation noise. These improvements are shown to enhance the prediction accuracy of the surrogate models, and further enhance the efficiency of optimization. Generally, compared to traditional surrogate models, fewer simulation evaluations would be needed to find the optimal solution when these improved models are applied.