Several Radial Basis Response Surface Constrained Optimization Algorithms For Solving Expensive Black-box Optimization Problems

Black-box function means that the analytical expression between the input and output of the function is difficult to obtain.Usually,it is necessary to run a very time-consuming computer simulation program for solving large-scale partial differential equations,or it is necessary to conduct engineering experiments and scientific experiments that consume a lot of manpower and material resources.The researches on solving its optimal points and optimal values have important practical significance.Aiming at these kind of expensive black-box optimization problems,this dissertation proposes several radial basis response surface optimization algorithms with constraints to solve these kind of expensive black-box optimization problems.The main contents are listed as follows:The first chapter briefly introduces the research background and significance of this dissertation and the current research status of algorithms for solving black-box optimization problems in Chinese and abroad.The second chapter introduces a commonly used model for solving black-box optimization problems,and design of experiments that always applied to generate initial points before the model is established,then the main research contents of this dissertation is proposed.Chapter 3 proposes a radial basis function response surface model optimization algorithm for solving black-box optimization problems � adaptive sampling response surface constrained optimization algorithm.The adaptive sampling response surface constrained optimization algorithm early adopts the form of circularly selecting elements in the given search pattern vector to take into account the local search and the global search,and then by calculating the distance between the global optimum of the response surface model of the previous iteration and that of the current iteration,the sampling point of this iteration and the search type of the next iteration are selected adaptively.Such a processing method could be more effectively to balance the local search and the global search.Numerical experimental results show that the proposed adaptive response surface constrained optimization algorithm has certain advantages.Chapter 4 proposes a combined response surface constrained optimization algorithm based on the proposed adaptive sampling response surface constrained optimization algorithm.The algorithm uses a combination model of two radial basis function models.The two radial basis function models are cubic radial basis function model and thin plate spline radial basis function model.Since the adaptive sampling response surface constrained optimization algorithm uses a cubic radial basis function to establish a response surface model,the accuracy of the model established by this selection is limited.By combining the form of the response surface models,the fitting accuracy and the stability of the model can be improved.Numerical results in the test problems also show that the stability of the algorithm has been significantly enhanced.Chapter 5 proposes an adaptive sampling and combining response surface global optimization algorithm for solving black-box optimization problems with some expensive constraints.The algorithm uses a two-stage algorithm framework that is the same as that used in the first stage of the radial basis function-based constrained global optimization algorithm.The second stage adopts the sampling technique of the combined response surface constrained optimization algorithm.Experimental results demonstrate the adaptive sampling and combining response surface global optimization algorithm is better than similar two-stage framework algorithms.