Simulation-based dynamic origin-destination matrix estimation on freeways: A Bayesian optimization approach

This study focuses on dynamic origin-destination demand estimation problem on freeway networks. Existing studies on this problem rely on high-coverage of traffic measurements and assumptions on travel times, exhibiting limitations in real-world applications. We formulate the problem as a bi-level programming model, where micro-simulations are incorporated to precisely model traffic flows/travel times on freeways. The bi-level programming model cannot provide explicit closed-form expressions for the objective function and its derivatives, and also intrinsically high-dimensional. Thus, it is highly challenging to find efficient solution algorithms. In this regard, a problem-specific and computationally efficient Bayesian optimization approach is designed. Herein, a novel surrogate model is proposed by embedding a physical surrogate model (it characterizes underlying physical mechanisms and provides global yet less precise approximations) into a functional surrogate model (it provides precise local approximations). The embedding provides problem-specific knowledge for the surrogate model. More importantly, it also restricts the feasible region, enabling the surrogate model to efficiently deal with high-dimensional problems. Gaussian process can be served as the functional surrogate model. Two linear physical surrogate models are proposed to capture interactions between travel demand and traffic measurements. To deal with constraints in the surrogate model, a projection-distance based acquisition function is designed. In searching for new points, the proposed acquisition function is capable of assigning unique weight of exploration to each feasible solution. The proposed approach is validated based on a freeway corridor example, which indicates its outperformance over existing dynamic origin-destination estimation methods in terms of computational efficiency and solution accuracy.