工程数值优化方法研究进展

ADVANCES IN NUMERICAL OPTIMIZATION METHODS

回顾与分析了工程数值优化方法研究的发展历程 ,着重介绍与讨论了优化问题的几种数学列式、近似问题的保真度与近似函数 ,以及复杂优化问题的求解策略等。指出优化问题的对偶列式变式 DFOP-V2与高精度多点近似函数和二级近似概念结合而产生的数值优化解法 ,具有通用性 ,高的计算效率 。

This paper reviews mainly the advances in numerical optimization methods developed since the late eighties of the 20th century for complex optimization problems in engineering. It focuses on several critical aspects of the optimization methodology including mathematical formulations, approximation functions and solution strategies for optimization problems. And a concept of fidelity for approximate problems and its significance are presented and discussed. It is pointed out that the formulation DFOP V2 based on the dual theory and envelope function is superior to other formulations in respects of simplifying optimization procedure and raising computational efficiency, especially for large scale problems; as compared with Taylor expansions, multi point approximate functions may approach the original functions with high quality in a wide region of design variable space; and the solution strategy of two level approximation concept is much beneficial to solving complex problems with high non linearity. Suggestions are given for further developing numerical optimum methods which are of convenience and efficiency in applications for engineers.