Research And Application Of Gaussian Process Assisted Global Optimization

With the continuous development of modern CAE technique, all kinds of global optimization methods have been widely applied in fields of automobile body design and sheet forming. Objective functions of automobile body design and sheet forming optimization are generally complicated implicit black-box, the complexity of which manifests itself as multivariable, strong nonlinear, strong coupling characteristic and multimodality. For such problems, pure traditional gradient algorithm and heuristic algorithm were both hard to satisfy the application requirement of practical engineering in terms of computational efficiency. In recent twenty years, in order to improve the optimization efficiency, metamodel technique based optimization has become an effective mean for such optimization problems. However, with the improvement of problem dimensions and complexity, sample numbers are growing exponentially, efficiency and the building of high accuracy metalmodel become the main bottlenecks of the metamodel-based optimization. As a result, how to use limited samples to build metamodel with high accuracy is the prerequisite to ensure the wide improvement of complicated optimization problem convergence rate. In conclusion,this paper pursues research on the basis of Gaussian process metamodel-based global optimization. Detailed research contents are as follows.(1) This paper will revise EGO proposed by Jones from two aspects. We proposed efficient global optimization method based on cross validation to make up the deceit effect caused by initial sample distribution.Firstly, considering the diversity of samples, this paper divided iterating samples into groups to improve diversity of agent model in design space and probability of the overall samples by using the idea of cross validation. Secondly, taking the diversity of samples into consideration, we use the Euclidean distance between the current and new samples to build the diversity rules. When EGO falls into the regions in which the curvature of objective function is small or there is topical peak, the algorithm can base on the diversity rule to realize the global optimization in sparse samples regions by using less iterating times.Comparing with the main EGO, the biggest advantage of this method is that it ensures the diversity of the subsequent samples. As a result, it will avoid falling in local convergence under the circumstance of considerable samples.(2) For the high-dimensional and strongly charateristics of sheet metal formingoptimization problems after introducing the time design variables, this paper proposes a high dimension and global optimization method called GPFA(Gaussian process metamodel-based firefly algorithm), which is based on Gauss process metamodel. The biggest advantage of this method is that it can build searching engine based on Gauss process metamodel. Combining EI(expected improvement), it can also select training samples creating by firefly algorithm in order to generate new samples automatically.With this mode, we can ensure that the optimization searching can focus on the smaller region including the optimum point. As a result, we are able to improve the optimization efficiency as well as the robustness of convergence. This paper takes twenty dimension functions to test the GPFA method and compares it with EGO and firefly algorithm. The test result shows that GPFA method leads to a fast and robust convergence of the optimization process.