Bayesian optimization techniques for high-dimensional simulation-based transportation problems

Bayesian optimization (BO) is an attractive method for tackling transportation optimization problems due to its ability to balance exploitation and exploration. However, scaling BO to solve high-dimensional problems is a major challenge which has remained unsolved. Since transportation problems can be high-dimensional, the use of BO to solve transportation problems has been limited. This paper explores the use of BO with Gaussian process (GP) models to tackle high-dimensional transportation problems. It proposes formulations of the prior mean function and covariance function of the GP that enable BO to incorporate problem-specific transportation information, while remaining computationally tractable. This is done through the use of an analytical surrogate model. We validate the method with the 1-D and 100-D Griewank functions. The impact of different forms of bias in the surrogate model was also evaluated using the 100-D Griewank function example. We then apply the method to a high-dimensional traffic signal control problem in New York City. The results indicate the added value of using the problem-specific information in the prior mean and/or the covariance function. Importantly, for surrogate models that are not accurate approximations of, but have significant (anti-)correlation with the true objective function, the better approach is to embed the information in the covariance function, rather than in the prior mean function. More generally, the use of problem-specific information in the covariance function is robust to the accuracy of the surrogate model. This opens the way for a variety of low-resolution analytical transportation models to be used to tackle high-dimensional simulation-based optimization problems.