A hybrid algorithm for the dimensional synthesis of parallel manipulators

Increasing the number of non-dominated solutions among multiple objectives is beneficial for determining the optimal comprehensive performance of parallel manipulators (PMs). In engineering, we often achieve this by increasing the population size of intelligent optimization algorithms, which leads to an exponential increase in computational costs, especially for high computationally intensive objective functions. How to increase the number of non-dominated solutions without significantly increasing computational costs is a challenge faced by the dimensional synthesis of PMs. A hybrid algorithm combing particle swarm optimization (PSO) and direct search algorithms was proposed in this work to fix this issue. And, a procedure for direct search algorithm to determine the Pareto optimal front is proposed. The proposed hybrid algorithm is implemented in three steps: (1) The design parameter space is coarsely meshed to determine the amplitude of objective functions to achieve its dimensionless purpose; (2) the PSO algorithm is adopted to obtain the approximate Pareto front, as well as the Pareto front hypersurface stretched by the optimal design parameter space; (3) the neighborhood of the approximate Pareto optimal set was finely meshed, and the direct search algorithm is proposed to update the non-dominated solutions that are closer to the real Pareto front. The proposed hybrid algorithm can obtain more non-dominated solutions while avoiding the significant increase in computational costs caused by increasing population size. The proposed algorithm was implemented using the dimensional synthesis of the 2UPR-RPU PM. Compared with the PSO algorithm, which produced 80 sets of non-dominated solutions, the proposed hybrid algorithm generated 242 sets of solutions with the computational costs only increased 32%.