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中文摘要：
在动态多目标优化中，各目标通常相互冲突，其最优解往往有无穷多个，如何在时间连续发生变化的情况下依然能求出分布均匀且数量多的Pareto最优解供决策者选择十分重要．对动态多目标优化问题连续变化的时间变量区间进行了任意划分，在得到的每个时间子区间上把动态多目标优化问题近似为静态多目标优化问题，进而在每个子区间上定义了种群的静态序值方差和静态密度方差，然后把目标个数任意的动态多目标优化问题转化成一个双目标静态优化问题．在给出的一种能自动检测时间变化的自检算子下，提出一种新的动态多目标优化进化算法，并且证明了算法的收敛性．计算机仿真表明新算法对动态多目标优化问题求解十分有效．
英文摘要：
Dynamic multi-objective optimization problems （DMOPs） often involve incommensurable, competing and varying objectives with time, and the number of their optimal solutions is usually infinite. Thus how to find a sufficient number of uniformly distributed and representative Pareto optimal solutions under the condition of the continuously changing time for the decision maker is very important. In this paper, the continuously changing time period of DMOPs is divided into several random subperiods. In each subperiod, the dynamic multi-objective optimization problem is approximated by a static multi-objective optimization problem. At the same time, the static rank variance and the static density variance of the population is defined in each subperiod. Then, by using the static rank variance and the static density variance of the population, the dynamic multi-objective optimization problem with random objective functions is transformed into a bi-objective static optimization problem. A new dynamic multi-objective optimization evolutionary algorithm is proposed based on a new self-check operator which can automatically check out the time variation and its convergence is proved. The simulations are made and the results demonstrate the effectiveness of the proposed algorithm.
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