单峰函数最优化问题的进化策略

１．引言 考虑无约束优化问题ｆ（ｘ），其中ｆ（ｘ）为单峰函数．这类优化问题，不仅包含具有某种凸性的函数的极小化问题，而且包含其它许多问题，例如相容的和不相容的线性方程组的求解，也都可以归结为这类优化问题． 如果函数ｆ（ｘ）的性态良好，各类以梯度为基础的算法无疑是求解问题（Ｐ）的首选方法．假若问题（Ｐ）不可微，或者虽然可微，但 ｆ（ｘ）的 Ｈｅｓｓｉａｎ阵高度病态，则应该另辟蹊径． 近年来颇受人们重视的进化类算法，由于不使用梯度，计算过程对函数的性态依赖性较小，具有适应范围广、鲁棒性强的优点，而且特别…

AN EVOLUTIONARV STRATEGY FOR MINIMZING UNIMODAL FUNCTIONS

In this paper, a new evolutionary strategy is proposed for minimizing uni- modal functions. Main characteristic of the strategy is that the classical mutation operator-Gaussian distribution is substituted by an uniform distribution. Theoretical analysis and numerical experiments indicate that convergence rate of the new strategy is superior to the classical one in most cases. Criteria of adoption of parent population and verification of step-length are also studied, and computa- tional efficiency of evolutionary strategies, in which crossover operator is employed or unemployed, is compared.