Hybrid algorithm for multi-objective optimization design of parallel manipulators

Abstract

In this paper, a hybrid algorithm was proposed for multi-objective optimization design with high efficiency and low computational cost based on the Gaussian process regression and particle swarm optimization algorithm. For the proposed method, the global performance indices, including regular workspace volume, global transmission index, global stiffness index, and global dynamic index were considered as objective functions. First, the multi-objective optimization problem considering the boundary conditions, objective, and constraint functions was constructed. Second, the Latin hypercube design was regarded as the design of experiment to obtain the computer sample points. Besides, the high-precision objective-function values were obtained by increasing the node density in the workspace at these sample points to provide sufficient information for the mapping model. Third, the Gaussian process regression was proposed to build the mapping model between the objective functions and the design parameters, thus reducing the computational cost of global performance indices. Cross-validation and external validation were adopted to verify the mapping model. Finally, the hybrid algorithm combined with the Gaussian process regression and particle swarm optimization algorithm was proposed for multi-objective optimization design. The 2PRU-UPR parallel manipulator was taken as a case to implement the proposed method (where P was a prismatic joint; R a revolute joint; U a universal joint). The comparison from the back propagation neural network, multivariate regression, and Gaussian process regression mapping models showed that the Gaussian process regression model had higher accuracy and robustness. The proposed hybrid algorithm saved 99.84% of computational cost compared to using the particle swarm optimization algorithm. The Pareto frontier of the multi-objective optimization problem of the 2PRU-UPR parallel manipulator was also obtained. After optimization, the performance indices were significantly improved.