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.

在本文中，一个混合算法提出了多目标优化设计，具有高效率和低计算成本基础上的高斯过程回归和粒子群优化算法。对于所提出的方法，全局性能指标，包括规则工作空间体积、全局传输指标、全局刚度指标和全局动态指标被视为目标函数。首先，构建了考虑边界条件、目标函数和约束函数的多目标优化问题。其次，拉丁超立方设计被认为是获得计算机样本点的实验设计。此外，通过增加这些样本点工作空间中的节点密度来获得高精度的目标函数值，为映射模型提供足够的信息。第三，提出了高斯过程回归来建立目标函数和设计参数之间的映射模型，从而降低全局性能指标的计算成本。采用交叉验证和外部验证来验证映射模型。最后，针对多目标优化设计，提出了结合高斯过程回归和粒子群优化算法的混合算法。所述2PRU-UPR并联机器人取作的情况下，以实施所提出的方法（其中，P是一个棱柱接头; R旋转接头; U A万向接头）。从反向传播神经网络、多元回归和高斯过程回归映射模型的比较表明，高斯过程回归模型具有更高的准确性和鲁棒性。与使用混合算法相比，所提出的混合算法节省了 99.84% 的计算成本粒子群优化算法。还得到了2PRU-UPR并联机械臂多目标优化问题的Pareto前沿。优化后，各项性能指标得到显着提升。