An optimization-based dynamic reordering heuristic for coordination of vehicles in mixed traffic intersections

In this article, we address a coordination problem for connected and autonomous vehicles (CAVs) in mixed traffic settings with human-driven vehicles (HDVs). The main objective is to have a safe and optimal crossing order for vehicles approaching unsignalized intersections. This problem results in a mixed-integer quadratic programming (MIQP) formulation, which is unsuitable for real-time applications. Therefore, we propose a computationally tractable optimization-based heuristic that monitors platoons of CAVs and HDVs to evaluate whether alternative crossing orders can perform better. It first checks the future constraint violation that consistently occurs between pairs of platoons to determine a potential swap. Next, the costs of quadratic programming (QP) formulations associated with the current and alternative orders are compared in a depth-first branching fashion. In simulations, we show that our heuristic can be a hundred times faster than the original and simplified MIQPs (SMIQPs) and yields solutions that are close to optimal and have better order consistency.