中文摘要：

高维多目标优化问题普遍存在且非常重要,但是,已有的解决方法却很少.本文提出一种有效解决该问题的融入决策者偏好的集合进化优化方法,该方法首先基于决策者给出的每个目标的偏好区域,将原优化问题的目标函数转化为期望函数;然后,以原优化问题的多个解形成的集合为新的决策变量,以超体积和决策者期望满足度为新的目标函数,将优化问题转化为2目标优化问题;最后,采用多目标集合进化优化方法求解,得到满足决策者偏好且收敛性和分布性均衡的Pareto优化解集.将所提方法应用于4个基准高维多目标优化问题,并与其他2种方法比较,实验结果验证了所提方法的优越性.

英文摘要：

Many-objective optimization problems are common and important in real-world applications, previous theories and methods suitable for them, however, are few so far. We presented a set-based many-objective evolutionary optimization algorithm with integrating a decision-maker＇ s preferences to effectively solve the problems above in this study. In the proposed method, each objective function of the original optimization problem was first transformed into a desirability function based on preference areas given by the decision-maker over it; thereafter, the optimization problem was further transformed into a bi-objective optimization one by taking such indicators as hyper-volume and the decision-maker＇ s satisfaction as two new objectives in which a set formed by multiple solutions of the original optimization problem is as the new decision variable;finally, the transformed bi-objective optimization problem was solved by using a set-based evolutionary optimization algorithm to obtain a Pareto optimal set which meets the decision-maker＇ s preferences and balances the convergence and the distribution. The proposed method was applied to four benchmark many-objective optimization problems and compared with the other methods. The experimental results showed its advantages.