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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, which is an important research content of evolutionary computation and also a difficult research point.When the evolutionary algorithm searches for robust optimal solutions, Monte Carlo integral (MCI) approximation is usually used to estimate the effective (EOF), but due to the low accuracy of the existing original Monte-Carlo method (C-MC), the performance of the evolutionary algorithm searching for robust optimal solutions is poor.In this paper, we propose a quasi-Monte Carlo method (Q -MC) .Through a large number of numerical experiments, the results show that compared with C-MC, the Q-MC method introduced in this paper - SQRT sequence, SOBOL sequence and Korobov lattice can estimate EOF more accurately, and then Greatly enhance the performance of evolutionary algorithm search for robust optimal solution.