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

Abstract

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 trac. In order to maximize benets from these technologies on highway trac management, vehicle trajectories need to be not only controlled at the individual level but also coordinated collectively for a stream of trac. As one of the pioneering attempts to highway trac trajectory control, Part I of this study (Zhou et al., 2015) proposed a parsimonious shooting heuristic (SH) algorithm for constructing feasible trajectories for a stream of vehicles considering realistic constraints including vehicle kinematic limits, trac 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 trac performance measures on mobility, environment and safety. The computational complexity and mobility optimality of SH is theoretically analyzed, and veries 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 ndings. They show that vehicle trajectories generated from NG-SH signicantly 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.

Eco-Approach and Departure System for Left-Turn Vehicles at a Fixed-Time Signalized Intersection

“…The main idea is to iteratively find state x forward in time and then co-state λ backward in time. Interested readers could refer to these papers [9,18,35] for the detailed algorithm.…”

“…With the development of emerging communication and control technologies, eco-driving control which attempts to smooth the speed profile vehicles promptly became a hotspot of research. The relevant researches can be categorized into eco-driving on freeway [9,10,[12][13][14] and on signalized arterial [14][15][16][17][18][19][20]. Eco-driving on freeway mainly focuses on reducing the vehicles' velocity oscillation when they are following a leading vehicle.…”

“…Since these methods only concerned about the fuel and emissions saving of individual vehicle without considering its impact on following vehicles, they would have a poor ecological performance under heavy traffic and even negative effect on mobility. Thus, Li proposed a parsimonious shooting heuristic algorithm to force all connected and automated vehicles (CAVs) drive pass the intersection with the smallest headway with its preceding vehicle and run at posted speed limit to maximize both throughput and fuel saving [18,19]. Based on this idea, Jiang designed a similar system that is able to function under partially connected and automated vehicles environment by utilizing the impacts of connected and automated vehicles on conventional human-driven vehicles.…”

“…Barth and Xia simplified the optimization by modelling the acceleration and deceleration stage as trigonometric functions travel time to the intersection [16][17][18][19][20][21][22]. Rakha utilized simulation to generate various speed trajectories which comply with the constraints of signal control and then selected the trajectory with lowest fuel consumption as output [36].…”

“…Liu decomposed the original multi-stage optimal control problem into a sequence of optimal control sub-problems approximated by optimization models which contains few control variables [33]. Li designed a SH-based optimization framework to check the performance of feasible trajectory vector and output the vector when it is optimal [18]. These simplifications aim at avoiding the infinite dimension optimization problem with nonlinear objective and constraints to reduce the computation time.…”