Research Of Global Optimizationalgorithm Base On MetaModel

Mordern mechanical and electrical products become more and more complex, and it need more and more computing resource to simulate and analysis these products. Although computer technology developed rapidly, and the speed of computer become faster, it hard to meet the industry demand for simulation and analysis. It reported that an analysis of simulating automobile collision need36-160hours to simulate, and an optimization of2variables will cost almost from75days to11months. It is hard to acceptable in practical engineering applications. To deal with the challenges, the metamodel method was widely used in industry product design. This method could cut the simulation times of simulation without affecting the accuracy of simuation target model, and reduce the consumption of computing resources.The method of metamodel is that replace complex and expensive simulation target model with simplified model which constructed by sampling points generated through experiment design.The global optimization based on metamodel is that use metamodel to search global optimum and it include the research of design of experiment, metamodel, global optimization. This article will discuss the adaptively sequential sampling, DIRECT algorithm, and incremental metamodel and Pareto multi-objective optimization and it include this content as follows.1) Adaptively sequential sampling based on RBF metamodel. Because of hard to determin the number of sampling points, it is commonly unreasonable that construct metamode through one time sampling. To construct metamodel with a few points and overcome the defect of one time sampling method, adaptively sequential sampling increased points and make it at reasonable position as fas as possible. In order to utilize the geometrical feature of metamodel, maximum curvature of the response surface and minimum distance among the sampling sites, as a general sampling criterion, are adopted in sequential sampling procedure. For the simplicity of RBF model, we can easily evaluate curvature on design optimum via computing the difference and Hessian matrix. A new model approximation algorithm integrated sequential optimal sampling is presented. To illustrate the efficiency and accuracy of the proposed algorithm,5benchmark function and stress spring and weld beam problem have been tested, the result show that the new method is better than latin hyper-cube design and grid sampling.2) DIRECT algorithm based on metamodel. Based on deeply analysing the principle and convergence properties of DIRECT algorithm, to overcome the defect of DIRECT method, which is too much evaluation of objective function and slow convergence rate, a modified DIRECT method based on radial basis functions was proposed. The presented method identifies the optimum area containing the global or local optimum through analysing the information of sampling points. It enhances the convergence rate of DIRECT method through constructing the radial basis functions on the sampling points which collected from optimum area and searching global optimum on the metamodel. The presented method is applied to some numerical examples and a pressure vessel design and compare accelerated effects with5common metamodel.The results of these examples demonstrate that the best metamodel is RBF metamodel.3) A new global optimization method based on incremental metamodel. Based on research of incremental Latin Hyper-cube design and incremental updating of RBF metamodel. A new global optimization algorithm was proposed for the complex simulation model problem. To overcome the defect of old incremental latin hyper-cube sampling, which is hard to control the number of sampling points and limited to multiples, we proposed a improved incremental latin hyper-cube sampling method based on subtraction rule ideal. Combined incremental Latin hyper-cube sampling and the method of incremental update RBF metamodel, we proposed a new efficient global optimization algorithm. The presented method was applied in2commonly test functions and a weld beam problem. The results of the example demonstrated the efficiency and engineering practicability of the presented method.4) Multi-objective optimization based on metamodel. To overcome the defect of the old multi-objective opitimization based on metamodel which used single value metamodel, a subgoal function must construct a correspond metatmodel. We proposed the conception of response surface set; which utilize the linear feature of RBF metamodel and converte the coefficient vector to coefficient matrix, made multiple subgoals function mapping one metamodel. It was hard to directly calculate Pareto fitness of massive sampling points; In order to make full use of information of sampling points generated by last iteration and reduce the computational complexity of optimization algorithm, we proposed a new incremental updating method for calculate Pareto fitness, which overcomes the defect of large-scale matrix caused by excessive sampling points. A new multi-objective optimization algorithm based on metamodel integrated response surface set and method of incrementally calculating Pareto fitness is proposed. The presented method was applied two-bar truss design problem and I-beam design. The results of the example demonstrated the efficiency and engineering practicability of the presented method.Finally, the main research findings and innovations have been viewed and summarized at the end the article, and the challenges and future development of global optimization based on metamodel have been discussed.