Intensive interactions among vehicles at freeway on-ramp merging areas lead to congestion and accidents. The emergence of connected automated vehicles (CAVs) has shown great potential to improve this issue. In this paper, a mixed integer nonlinear programming (MINLP) model is proposed and solved for the task of a cooperative merging of two traffic streams at a freeway on-ramp merging section. The proposed model simultaneously optimizes multiple vehicles’ trajectories and their merging sequence to improve traffic efficiency and ensure safety. Unlike conventional treatments, which match one mainline facilitating vehicle with one merging vehicle, the proposed model determines the optimal number of facilitating vehicles and which mainline vehicles should serve as the facilitating vehicles to cooperatively minimize disruption from ramps. The safety and feasibility of the planned vehicle trajectories are guaranteed at any time. We propose an integrated solution algorithm that incorporates an iterative linear programming method into a novel search process based on a necessary condition for optimality that we identify and prove. The algorithm is highly efficient because it enjoys a significantly reduced search space. The proposed approach, consisting of the MINLP model and the solution algorithm, is evaluated under different traffic demands and mainline-ramp demand ratios and real vehicle arrival patterns from the NGSIM dataset. The performance of the proposed method outperforms benchmark CAV control algorithms, and the computational efficiency is promising for real-time automated merging tasks.