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标准NSGA-II算法

于 2022-03-07 发布 文件大小:153.77 kB
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NSGA2算法将在以下方面进行改进:1、快速的非支配排序    在NSGA进行非支配排序时,规模为N的种群中的每个个体都要针对M个目标函数和种群中的N-1个个体进行比较,复杂度为O(MN),因此种群中的N个个体都比较结束的复杂度为O(MN2),即每进行一次Pareto分级的时间复杂度为O(MN2)。在最坏的情况下,每个Pareto级别都只含有一个个体,那么需要进行N次分级所需要的时间复杂度则会上升为O(MN3)。鉴于此,论文中提出了一种快速非支配排序法,该方法的时间复杂度为O(MN2)。    该算法需要保存两个量:    (1).支配个数np。该量是在可行解空间中可以支配个体p的所以个体的数量。    (2).被支配个体集合SP。该量是可行解空间中所有被个体p支配的个体组成的集合。2、种群中个体多样性的保留    原始的NSGA算法中使用共享函数的方法来维持物种的多样性,这种方法包含一个共享参数,该参数为所求解问题中所期望的共享范围。在该范围内,两个个体共享彼此的适应度。但是该方法有两个难点:    (1).共享函数方法在保持多样性的性能很大程度上依赖于所选择的共享参数值。

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