多目标进化算法搜索鲁棒最优解效率研究-计算机工程与应用

Computer Engineering and Applications 计算机工程与应用 2011 ，47 (23 ) 29

⦾研究、探讨⦾

多目标进化算法搜索鲁棒最优解效率研究

任亚峰，郑金华

REN Yafeng ，ZHENG Jinhua

湘潭大学 信息工程学院，湖南 湘潭 411105

Institute of Information Engineering ，Xiangtan University ，Xiangtan ，Hunan 411105 ，China

REN Yafeng ，ZHENG Jinhua.Research on efficiency of multi-objective evolutionary algorithms in searching robust opti-

mal solutions.Computer Engineering and Applications ，2011 ，47 (23 )：29-33.

Abstract ：Robust optimal solution is of great significance in engineering application.It is one of the most important and dif-

ficult topics in evolutionary computation.Monte Carlo Integral (MCI )is generally used to approximate Effective Objective

Function (EOF )in searching robust optimal solution with Multi-Objective Evolutionary Algorithm (MOEA ).However ，due to

the low degree of accuracy in existing MCI method ，the performance of searching robust optimal solution with MOEA is

unsatisfactory.Therefore ，the Quasi-Monte Carlo (Q-MC )method is proposed which is used to estimate EOF.Through lots of

numerical experimentations ，the results demonstrate that the proposed Q-MC methods —Korobov Lattice can approximate

EOF more precisely when compared with the existing crude Monte Carlo (C-MC )method ，and consequently the efficiency of

searching robust optimal solution with MOEA has been improved at a substantial level.

Key words ：evolutionary algorithm ；robust optimal solutions ；Quasi-Monte Carlo method ；effective objective function ；Monte

Carlo integral

摘 要：鲁棒最优解是进化计算研究的重要方面，同时也是研究难点。多目标进化算法搜索鲁棒最优解时，通常要用蒙特卡罗积

分(MCI )近似估计有效目标函数(EOF )，而已有求解方法近似精度不高，使得算法搜索鲁棒最优解的性能较差。提出用拟蒙特卡

罗方法(Q-MC )来估计有效目标函数方法，其所引入的Q-MC 方法——Korobov 点阵能更精确地估计EOF 。实验结果表明，与现

有的原始蒙特卡罗方法(C-MC )相比，拟蒙特卡罗方法(Q-MC )可以较大地提高多目标进化算法搜索鲁棒最优解的效率。

关键词：进化算法；鲁棒最优解；拟蒙特卡罗方法；有效目标函数；蒙特卡罗积分

DOI ：10.3778/j.issn. 1002-8