Bayesian optimization for traffic sensor deployment: Integrating network flow estimation into location planning

Accurate network flow estimation (NFE) is essential for effective traffic management, with its performance highly reliant on optimal sensor placement. Traditional two-stage methodologies, which first optimize sensor locations using surrogate observability metrics and then train an estimation model, often lead to suboptimal performance. This study proposes a unified bi-level black-box optimization framework that jointly optimizes sensor deployment at the upper level and NFE model training at the lower level. The framework explicitly accounts for the zero-shot nature of NFE tasks by excluding unobservable link data from training and is compatible with various NFE models, with a transfer learning-based estimator used as a representative example. The resulting black-box integer optimization problem is solved efficiently using an Embedding Bayesian Optimization algorithm, further enhanced by a hybrid random dictionary generation method that improves the numerical stability of Gaussian process fitting. Experiments on the Nanjing real-world case and Eastern Massachusetts networks demonstrate substantial improvements in estimation performance compared to the traditional two-stage method, highlighting the framework’s scalability and transferability for optimizing sensor placement in intelligent transportation systems.