基于近似模型的非线性区间数优化方法及其应用

在不确定优化中,非线性区间数优化方法由于需要嵌套优化,造成计算效率低下而阻碍其应用于工程实际.本文提出了一种基于径向基函数近似模型的求解方法,以提高非线性区间数优化方法的计算效率.该方法利用拉丁超立方实验设计方法采样,建立目标函数和各约束的径向基函数近似模型.利用近似模型代替嵌套优化中的真实模型,再用非线性区间数优化方法进行求解,从而提高了非线性区间数优化方法的计算效率,使得该算法在工程应用方面成为可能.用一个测试函数验证了该方法的可行性,最后将方法应用于车身薄壁梁的耐撞性优化.

Approximation model based nonlinear interval number optimization method and its application

The nested optimization existing in the nonlinear interval number optimization will lead to a low efficiency. An efficient method is suggested to promote the efficiency based on approximation models using the radial basis functions. Firstly, the approximation models are created for the objective function and constraints with the samples obtained from Latin hypercube design method. The actual models are replaced by the approximation models and this approximate optimization problem is solved by the nonlinear interval number optimization method. The computation efficiency is improved greatly and whereby it seems possible to apply the nonlinear interval number optimization method to practical engineering problems. A numerical test is investigated to demonstrate the effectiveness of the present method, and this method is successfully applied to the structural crashworthiness optimization of a thin-wall beam.