Coordinate measuring machines (CMMs) play an important role in modern manufacturing and inspection technologies. However, the inspection process of a CMM is recognized as time-consuming work. The low efficiency of coordinate measuring machines has given rise to new inspection strategies and methods, including path optimization. This study describes the optimization of an inspection path on free-form surfaces using three different algorithms: an ant colony optimization algorithm, a genetic algorithm, and a particle swarm optimization algorithm. The optimized sequence of sampling points is obtained in MATLAB R2020b software and tested on a Leitz Reference HP Bridge Type Coordinate Measuring Machine produced by HEXAGON. This study compares the performance of the three algorithms in theoretical and practical conditions. The results demonstrate that the use of the three algorithms can result in a collision-free path being found automatically and reduce the inspection time. However, owing to the different optimization methodologies, the optimized processes and optimized times of the three algorithms, as well as the optimized paths, are different. The results indicate that the ant colony algorithm has better performance for the path optimization of free-form surfaces.