Advanced connected and automated vehicle technologies offer new opportunities for highway traffic smoothing by optimizing automated vehicle trajectories. As one of the pioneering attempts, this study proposes an efficient trajectory optimization algorithm that can simultaneously improve a range of performance measures for a platoon of vehicles on a signalized highway section. This optimization is centered at a novel shooting heuristic (SH) for trajectory construction that considers realistic constraints including vehicle kinematic limits, traffic arrival patterns, car-following safety, and signal operations. SH has a very parsimonious structure (e.g., only four acceleration parameters) and a very small computational complexity. Therefore, it is suitable for real-time applications when relevant technologies are in place in the near future. This study lays a solid foundation for devising holistic cooperative control strategies on a general transportation network with emerging technologies.