Research On Multi-objective Optimization Method Based On Kriging Surrogate Model

In the process of engineering structure optimization design,computer simulation technology is usually used to simulate the structure response.But as the complexity of the structure increases,the single calculation time will increase greatly.Using common intelligent algorithms such as simulated annealing algorithm and Genetic algorithms,etc.,need to calculate a large number of objective functions,which leads to an optimization design cycle that is too long,and even optimization is difficult to converge.By surrogate approximation instead of high realistic computer simulation optimization,the number of optimization calculations can be effectively reduced,and the optimization efficiency can be improved.In this paper,the dynamic update process of the surrogate is taken as the main research object,and the multi-peak parallel multi-point addition criterion for single target is proposed.For multi-objective optimization,a multi-objective optimization method based on Kriging is proposed.The impact of the initial sample points on the optimization of the agent model is analyzed.The specific research contents of this paper include:(1)For the influence of the initial sample points on the optimization process,this paper uses qualitative data to analyze the influence of the number of initial sample points and the distribution of initial sample points on the optimization results,and analyzes the applicability of the initial sample points to the dimensions of the optimization variables.The results show that the initial sample points have an important impact on the optimization results.If the initial sample points are too small,the optimization is easy to converge in advance,and the local minimum solution is obtained.If the initial sample points are too much,the calculation amount is too large,and the optimization efficiency of the dynamic surrogate is obtained.The more dispersed the initial sample points,the better the stability of the optimization;the number of sample points required for optimization increases as the dimension of the optimization variable increases.This paper makes reasonable suggestions for the selection of initial sample points.(2)As the multimodality of the proxy model update criterion function,a multi-peak search algorithm based on clustering adaptive elite individual is proposed,which is used to calculate multiple peaks of the dynamic surrogate update criterion function,and the surrogate is reconstructed by the new sample points and their response values at multiple peaks.This process is called parallel multi-peak multi-point plus point criterion.The multi-peak parallel multi-point update criterion proposed in this paper is tested by the mathematical test function,and its feasibility is verified.Compared with the commonly used EI plus point criterion,the optimization efficiency is improved by 66% to 180%.(3)For the multi-objective optimization problem,this paper combines the surrogate optimization method with the multi-objective genetic algorithm(NSGA-II),establishes the different Kriging models for different targets,and calculate the pareto of predictive response value of the Kriging models and the add-point criterion function value by NSGA-II.Select the sample points on the two pareto to update the Kriging to reduce the number of times the multi-objective genetic algorithm calculates the objective function.Select the sample points on the two pareto to update the Kriging to reduce the number of calculations of the objective function by the multi-objective genetic algorithm.The method proposed in this paper is tested by mathematical test function.The results show that the convergence and diversity of the optimal solution set are similar compared with the direct multi-objective genetic algorithm.However,the number of times the objective function is calculated in the previous method is only about 3% of the latter method.