The Kriging-based Global Approximation And Simulation Optimization Methods

The engineering system problems are more and more complex with the development of today’s science and technology. Therefore, there has been a wide variety of design research methods and ideas to optimize these problems. The approximate global optimization method based on response surface models is one of the current important engineering design studies. The research method mainly includes computer experimental design, modeling methods based on response surface, the optimal solution method for global approximate and optimization (one or sequential) according to information of response. Furtunately, it is very fast and efficient to solve expensive complex black-box approximate optimization model and computer simulation model.As a high-precision interpolation response surface model, Kriging can flexibly replace multimodal or nonlinear functions, estimate the "optimal parameters’ and approximately evaluate the model accuracy. Therefore, it is one of the currently extensive used response surface models. In the optimization process, the information from function values and the estimated variance of Kriging model can effectively guide the optimization search towards a more global region. Global approximate and optimization methods based on Kriging have been infused into project design, structural optimization, big data analysis and MDO, and also are widely applied to aerospace engineering, mechanical engineering, vehicle engineering, geological Engineering and other fields.The contributions on this dissertation are summarized as follows:(1) Incremental construction method based on Kriging model is studied after we deeply understand structure and parameters of the standard of Kriging. In the case of losing quite little precision, it can greatly improve the modeling efficiency. At the same time, it also provides the technical support for the proposed sequential global approximation method based on incremental Kriging.(2) A global approximation method, which aims to improve efficiency, is proposed in sequence optimization process due to the incremental Kriging method. First, the incremental construction of Kriging is researched in depth on the basis of making sure the stability and effectiveness of Kriging model. In addition, it uses the maximum variance method to search next sample point and determine which method (DACE or incremental modeling) will be used to consturct Kriging by appropriate update criteria.(3) A sequential Kriging-based optimization method, combining Kriging surrogate model, duality principle and trust region strategy to solve black-box unconstrained optimization problems, is studied. We firstly introduce the duality principle to transform the non-convex optimization problem based on Kriging model into a simple convex programing problem in order to quickly get accurate global minimums. Then, trust region strategy which can improve accuracy and convergence rate is adopted to find next evaluation point by searching an optimal solution from the transformed optimization problem.(4) A Kriging-based sequence global optimization method for multiple sampling points is put forward. The algorithm mainly introduces a deleting minimum middle distance criterion to obtain multiple sampling, and uses the improved generalized EGO as infill sampling criteria to optimize the multiple sampling points. The method enhances computational efficiency. Meanwhile, it can also effectively balance global and local search direction. Several tests show that the method is efficient and practical in engineering.(5) A new Kriging-based constrained global optimization algorithm is proposed. The algorithm can dispose black-box constrained problem even if all initial sampling points are infeasible. How to find a feasible point when there is no any feasible data in initial sample and how to obtain a better feasible point under the circumstances of fewer expensive function evaluations are two key issues.(6) In FlowComputer multidisciplinary design optimization platform, the simulation optimization module based on RSM component is developed by using open-source DAKOTA tookit. EGO method and the proposed optimization algorithms have been realized due to the design platform. Finally, a heavy car fuel economy simulation optimization problem is verified to illustrate effectiveness of the proposed methods.