Abstract: 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 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