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Numerous fast heuristic algorithms, including shooting heuristics (SH), have been developed for real-time trajectory optimization, although their optimality has not yet been quantified. This paper compares the performance between fast heuristics and exact optimization models. We investigate a core trajectory optimization problem as a building block for numerous trajectory optimization problems, i.e., guiding movements of connected automated vehicles on a one-lane highway when the arrival and departure times and velocity are given. To apply the SH algorithm to this problem, we adapt it to a fast-simplified shooting heuristic (FSSH) model to solve the trajectory smoothing problems with different arrival and departure velocities. An exact trajectory optimization (ETO) model is formulated that takes the vehicle position and velocity as the decision variables, and the fuel consumption and driving comfort as the objective function. The constraints of the model are based on the limits and safety of the vehicle dynamics between consecutive vehicles. We demonstrate the convexity of the ETO objective function, ensuring the solvability of the ETO model at the true optimum using gradient descent algorithms supplied by the MATLAB optimization toolbox. Six groups of numerical experiments using different input parameters and one experiment using real Next Generation Simulation (NGSIM) data are conducted. ETO can improve the objective values by a few to tens of percentage points. However, FSSH achieves a greater solution efficiency with an average solution time of less than 0.1 s compared to ~450 s for ETO.
Xu et al. (Mon,) studied this question.