Researches On Surrogate-based Global Optimization Algorithm Based On Kriging Model

With the rapid development of the world economy and the increasingly fierce market competition,companies are urgently required to provide short-cycle,low-cost,high-quality products to enhance their global competitiveness.From the perspective of modern quality engineering,product quality is determined by design and design phase is the headstream of improving product quality.Otherwise,with the development of simulation modeling technology,numerical computation technology and computer hardware and software,high-precision simulation models are widely used in the design optimization of complex products and systems.But the high-precision simulation models are often computationally expensive and will be run repeatedly during the optimization process,which make the high simulation cost be a bottleneck restricting the efficiency of modem design optimization.In order to improve the design efficiency,reduce the design cost and cycle time of complex products and systems,the approximate optimization methods based on surrogate models have received much attention from researchers at home and abroad.Surrogate models are simple approximate mathematical models constructed using small-sample simulation results,and are used to substitute expensive simulation models in the process of analysis and design optimization.Via constructing surrogate models and designing reasonable optimization strategies,surrogate-based optimization methods enable the optimization to converge to the optimal solution with much less computational burden and few design cycles.The surrogate-based optimization process mainly involves design of experiment,surrogate modeling,adaptive optimization strategies and their infill sampling criteria.For complex black-box optimization problems,in this paper,we present a systematical study on surrogate-based optimization algorithms for constrained optimization problems,determined and stochastic multi-objective optimization problems,and parallel simulation optimization problems,using the techniques and means such as system simulation,Kriging technique,heuristic optimization algorithms and empirical research.The main contelts are summarized as follows:(1)Analysis on Kriging-based adaptive optimization mechanism.For Kriging-based optimization algorithms,we firstly introduce the Kriging modeling technique in detail and give suggestions for selecting its internal parameters.Then,the adaptive optimization mechanism of surrogate-based optimization algorithms,its features and key technologies are demonstrated through examples.In the end,the sub optimization problems,emerged in the surrogate-based optimization process,are pointed out and problem-solving methods are provided.This part provides a theoretical basis for the follow-up sections,and it is also beneficial for engineers to understand,use and develop surrogate-based optimization algorithms.(2)Constrained surrogate-based optimization algorithm based on Kriging model and a bi-objective constraint-handling strategy.When the optimization problem contains black-box constraints,the constraint-handling strategy directly affects the accuracy and efficiency of the surrogate-based optimization algorithm.In this dissertation,based on the technique of taking constraints as optimization goals in evolutionary algorithms,we propose a two-objective constraint-handling strategy that can balance searching for the best objective value and learning the boundaries of feasible regions.Compared to penalty function methods,which are computational complex and require careful fine-tuning of the penalty factors,the numerical results show that,the optimization algorithm based on the proposed bi-objective constraint-handling strategy is more accurate and well-adapted.(3)Surrogate-based multi-objective optimization algorithm based on Kriging and its convergence assessment.For deterministic multi-objective optimization problems,we propose a Kriging-based multi-objective optimization algorithm,which optimizes the multi-objective problems by means of improving the quality indicator of the Pareto set.This algorithm firstly uses the probability of feasibility(PoF)criterion to identify the feasible regions and get an initial approximated Pareto set.Then,the PoF is combined with the expected hypervolume improvement criterion to continually improve the quality of estimated Pareto set.Otherwise,the convergence of the proposed algorithm is assessed by quantifying uncertainty on the estimated Pareto set based on conditional simulations.Finally,the numerical results indicate that the proposed algorithm is suitable for non-connected and non-convex optimization problems and also provides a new way to evaluate the convergence of the algorithm when the true Pareto set is unknown.(4)Estimation of the Pareto front and measuring its uncertainty in stochastic simulation through stochastic Kriging.In view of the fact that the interpolation property of Kriging model is not suitable for stochastic simulation,this dissertation proposes a multi-objective optimization algorithm based on stochastic Kriging.Firstly,the number of simulation replications for each design point is set by estimating the half-width of the confidence interval for the average simulation output.Then,the ability of stochastic Kriging to filter random noises is used to design a multi-objective optimization strategy for estimating the Pareto front.In the end,the variability,caused by the random noises of stochastic simulation,of the estimated Pareto front is quantified by nonparametric bootstrap method.The results of numerical examples and inventory simulation show that the proposed surrogate-based optimization algorithm is an effective method to support multiple criteria decision-making in stochastic systems.(5)Multi-point sampling criterion and parallel optimization algorithm for parallel simulation based on Kriging model.With the advances of parallel computing(simulation)techniques,designing of reasonable multi-point sampling criteria that can choose multiple design points simultaneity,is a new way to improve the efficiency of design optimization.In this dissertation,the q-EI multi-point sampling criterion is first extended to constrained optimization problems.And then,a new multi-point sampling criterion is proposed based on multi-objective strategy and clustering method.Finally,the effectiveness and efficiency of the surrogate-based parallel optimization algorithm,based on the proposed multi-point sampling criterion,is verified by comparing with other parallel algorithms.Finally,the dissertation also discusses some challenging topics in surrogate-based optimization algorithm research which deserve further research in the future,based on the above research results.