Parsimonious shooting heuristic for trajectory design of connected automated traffic part II: Computational issues and optimization

Advanced connected and automated vehicle technologies enable us to modify driving behavior and control vehicle trajectories, which have been greatly constrained by human limits in existing manually-driven highway traffic. In order to maximize benefits from these technologies on highway traffic management, vehicle trajectories need to be not only controlled at the individual level but also coordinated collectively for a stream of traffic. As one of the pioneering attempts to highway traffic trajectory control, Part I of this study (Zhou et al., 2016) proposed a parsimonious shooting heuristic (SH) algorithm for constructing feasible trajectories for a stream of vehicles considering realistic constraints including vehicle kinematic limits, traffic arrival patterns, car-following safety, and signal operations. Based on the algorithmic and theoretical developments in the preceding paper, this paper proposes a holistic optimization framework for identifying a stream of vehicle trajectories that yield the optimum traffic performance measures on mobility, environment and safety. The computational complexity and mobility optimality of SH is theoretically analyzed, and verifies superior computational performance and high solution quality of SH. A numerical sub-gradient-based algorithm with SH as a subroutine (NG-SH) is proposed to simultaneously optimize travel time, a surrogate safety measure, and fuel consumption for a stream of vehicles on a signalized highway section. Numerical examples are conducted to illustrate computational and theoretical findings. They show that vehicle trajectories generated from NG-SH significantly outperform the benchmark case with all human drivers at all measures for all experimental scenarios. This study reveals a great potential of transformative trajectory optimization approaches in transportation engineering applications. It lays a solid foundation for developing holistic cooperative control strategies on a general transportation network with emerging technologies.