基于拟蒙特卡罗方法的进化算法搜索鲁棒最优解的性能提高研究

Research on Increasing the Performance of Evolutionary Algorithm in Searching Robust Optimal Solutions Based on Quasi-Monte Carlo Method

鲁棒最优解在工程应用中具有十分重要的意义,它是进化计算的重要研究内容,也是研究难点.进化算法搜索鲁棒最优解时,通常使用蒙特卡罗积分(MCI)近似估计有效目标函数(EOF),但由于现有的原始蒙特卡罗方法(C-MC)近似精度不高,导致进化算法搜索鲁棒最优解的性能较差.文中提出用拟蒙特卡罗方法(Q-MC)估计有效目标函数.通过大量的数值实验,结果表明,与C-MC相比,文中所引入的Q-MC方法——SQRT序列、SOBOL序列和Korobov点阵能更精确估计EOF,进而较大提高进化算法搜索鲁棒最优解的性能.

Robust optimal solution is of great significance in engineering application. It is one of the most important and difficult topics in evolutionary computation. Monte Carlo Integral （MCI） is generally used to approximate effective objective function （EOF） in searching robust optimal solution with evolutionary algorithm （EA）. However, due to the low accuracy in existing crude Monte Carlo （C-MC） method, the performance of searching robust optimal solution with EA is unsatisfactory. Therefore, a Quasi-Monte Carlo （Q-MC） method is proposed to estimate EOF. The experimental results demonstrate that the proposed Q-MC methods -SQRT sequence, SOBOL sequence and Korobov Lattice approximate EOF more precisely compared with C-MC method, and consequently, the performance of searching robust optimal solution with EA is improved.