基于信赖域的动态径向基函数代理模型优化策略

Optimization Strategy Using Dynamic Radial Basis Function Metamodel Based on Trust Region

为了提高飞行器等复杂工程系统的设计质量与优化效率,基于代理模型的优化得到广泛应用。将信赖域思想引入基于代理模型的优化中,提出基于信赖域的采样空间更新策略,进而发展了一种基于信赖域的动态径向基函数代理模型优化策略(Trust region based dynamic radial basis function,TR-DRBF)。通过Maximin拉丁超方试验设计方法选取样本点,选用径向基函数方法构造代理模型,采用全局优化算法对所构造的代理模型进行优化,根据已知信息进行信赖域采样空间更新,在其内部选取新增样本点并更新代理模型,直至优化收敛。将本优化策略用于标准数学测试算例和工字梁设计优化实例,并与国内外现有研究成果进行比较,证明了TR-DRBF在优化效率和全局收敛性方面都有较好的表现,尤其是针对高维优化问题时,TR-DRBF具有更显著的优势。

To improve the design quality and optimization efficiency of complicated engineering systems such as flight vehicle, metamodel based optimization is applied widely. Trust region is imported into the metamodel optimization and the updating strategy for sampling space using trust region is proposed and then the optimization strategy using dynamic radial basis function metamodel based on trust region is proposed. The metamodel is constructed with radial basis function and initial sampling points selected by Maximin latin hypercube design method. Global optimization algorithm is employed to optimize current metamodel to find the potential global optimum of the true optimization problem. According to the current known information, the trust region sampling space is updated. During optimization process, the new sampling points in the trust region sampling space are added, and the metamodel is updated, until the potential global optimum of the true optimization problem is satisfied the convergence conditions. The optimization strategy is validated by using five benchmark numerical test problems and an I-beam design problem. As the optimization results shown, the capability of TR-DRBF in both aspects of optimization efficiency and global convergency is good compared with the study fruit inland and overseas at present. Especially for high dimension problems, the performance of TR-DRBF is appealing.