Global Optimization Methods Based On The Radial Basis Function (RBF) Response Surface Models

Since the objective function values of a typical black-box optimization problem are computed by calling and running the simulation tools,there is also a lack of clear structure information between the input and output of the system and it can be only realized by the time-consuming computer simulation,that cause the whole optimization process speed is very slow.Based on the above difficulties,it has been the important topic of mutual interest in the engineering,finance and other fields.This paper studied an adaptive framework and an improved stochastic radial basis function algorithm that are based on response surface models to solve black-box global optimization problems,they are both designed to use as little the number of iterations as possible to get the approximation solution of the global optimal point of the original objective function.The main results,obtained in this dissertation,may be summarized as follows :In chapter 1,we give brief introduction to the research significance of black-box global optimization problems,and summarize the research situation of a few kinds of derivative-free global optimization methods,then we outline the main research content of this article.In Chapter 2,we study a novel ADaptive Framework using Response Surface(ADFRS)to solve black-box global optimization problem,it take part in the optimization process by constructing the surrogate model of actual objective function.The main iteration steps of the ADFRS algorithm is consist of two phases.The first phase implement a mixture of local search and global search search strategy to guidance algorithm to explore the area where the global minimizer of objective function located,the second phase perform local search in the vicinity of the current best sample point to search for a better approximate solution.In the first phase,the approximate degree of two consecutive response surface models is identified to decide whether to choose the global optimal point of the current response surface model as the next iteration point,the strategy can make the algorithm to get a better improvement point faster.In the local search,the constraint range of next iteration point is restrained in the vicinity of global optimal point of current response surface model,the search radius around the global optimal point is dynamically vary with the distribution of the sample points,which ensures that the iteration point achieved by algorithm can be very close to a local minimum point of the original objective function in the local scope.Finally,the numerical experiment results show the effectiveness of our proposed methods.In Chapter 3,we study an IMproved Stochastic Response Surface(IMSRS)algorithm with radial basis function whose framework is similar to the ADFRS algorithm framework.IMSRS algorithm randomly generates a lot of trial points,and then use some methods to select points from the generated points as the next iteration points.In the local search,the algorithm randomly generates trials points in the neighborhood of the global minimizer of response surface model that obey normal distribution;in the global search,the trial points are randomly generated in the whole feasible region that obey uniform distribution.In the numerical experiment,the algorithm obtains satisfactory results compared with several effective stochastic radial basis function(RBF)algorithms.