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This paper studies a problem of designing trajectories of a platoon of vehicles on a highway segment with advanced connected and automated vehicle technologies. This problem is very complex because each vehicle trajectory is essentially an infinite-dimensional object and neighboring trajectories have complex interactions (e.g., car-following behavior). A parsimonious shooting heuristic algorithm is proposed to construct vehicle trajectories on a signalized highway segment that comply with boundary conditions for vehicle arrivals, vehicle mechanical limits, traffic lights and vehicle following safety. This algorithm breaks each vehicle trajectory into a few sections that are analytically solvable. This decomposes the originally hard trajectory design problem to a simple constructive heuristic. Then we slightly adapt this shooting heuristic algorithm to efficiently solve a leading vehicle problem on an uninterrupted …