Hybrid Global Optimization Algorithm Based On Dynamic Kriging Model And Gradient Projection Method

As electronic packaging equipments pursuing high speed and high precision,the dynamic optimization design of high-speed low-load mechanism has become a challenging research topic.Due to the coupling of rigid motion and elastic deformation,the dynamic model of highspeed low-load mechanism is usually a group of high-dimensional differential equations with time-varying coefficients and non-smooth nonlinearity,which is the great difficulty for modeling,analysis and optimization.If a series of dynamic optimizations of high-speed lowload mechanism regarded as black-box optimizations commonly existing in engineering,it provides a new way for the optimization of the complex high-speed low-load mechanism.So far,metamodel based optimization method combining metamodel technique and heuristic algorithm is an effective approach to solve black-box expensive optimizations.However,because the existing researchs tend to focus on accuracy,efficiency or stability,their proposed algorithms with poor comprehensiveness can not meet the requirement of engineering applications.Therefore,it is necessary to build a global optimization algorithm with strong comprehensiveness.In conclusion,this paper conducts research on the basis of metamodel based optimization methods.Firstly,the review of metamodel based optimization methods are illustrated.Secondly,based on the theroy of genetic algorithm(GA),Kriging model and gradient projection method,a hybrid global optimization(HGO)algorithm is proposed after some control parameters are selected.The proposed HGO algorithm includes two following innovations:(1)A new combination of dynamic Kriging model and GA is proposed.In the optimization,the samples of Kriging model are limited and the accuracy of each individual is repeatly evaluated by Kriging model.If accurate,the objective value predicted by Kriging model is used as the individual fitness value,otherwise the actual response value calculated by black-box function is used as the individual fitness value.The combination tries to ensure the accuracy of the possible optimal individual in each generation of the population,so as to improve the efficiency and accuracy of the optimization.(2)A mutation strategy based on modified gradient projection method is proposed.For the problem that GA can not handle nonlinear constraints effectively,the idea of gradient projection method is introduced into GA.Since a mutation strategy based on modified gradient projection method is proposed,the gradient predicted by the Kriging model is used to guide individuals to mutate.The mutation strategy not only effectively handles nonlinear constraints,but improve the local convergence of the algorithm.Then,in order to verify its effectiveness,two benchmark functions with different kinds of constraints are used to test the abilities of HGO.The test results show that HGO can take into account the accuracy,efficiency and stability to achieve a better comprehensive performance.Finally,in order to reflect its engineering practicability,HGO is employed to a dynamic response optimization of a space manipulator.The optimization results imply that HGO can play a better comprehensive performance and effectively solve the expensive blackbox optimizations in engineering.