Solving connected automated vehicle merging problems: A generalized benders decomposition-based approach for mixed-integer nonlinear programming

Intensive interactions among vehicles often lead to congestion and accidents, particularly at freeway merging sections. As connected automated vehicles (CAVs) become a reality, their collaborative driving offers a promising solution. However, the real-time scheduling and trajectory planning for multiple CAV streams remain challenging and are not adequately addressed in the existing literature. To this end, this study formulates an integrated mixed-integer nonlinear programming (MINLP) model to jointly optimize lane change decisions, vehicle sequences, and vehicle trajectories, with the objective of maximizing traffic efficiency and driving comfort at multi-lane freeway merging sections. Existing commercial software struggles to handle such a complicated model. To rapidly obtain solutions, this study designs a Generalized Benders Decomposition (GBD)-based solution algorithm to tackle the problem of multi-vehicle combinatorial optimization and nonlinear trajectory optimization. Meanwhile, the finite convergence property of the GBD approach is proved. Numerical experimental results demonstrate that the proposed model outperforms three benchmark CAV control methods and a two-step method under various traffic demands and mainline-ramp demand ratios, highlighting significant traffic benefits from jointly planning lane changes and driving sequences, as well as utilizing microscopic vehicle information. Furthermore, this study evaluates traffic delay and the number of lane changes under varying road lengths, i.e., the lengths of lane-changing and merging areas, identifying recommended lengths for the maximum traffic efficiency, and analyzing the performance trend under varying traffic demands.