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閱讀Book: MultiObjective using Evolutionary Algorithms (5) ---- Non-Dominated Sorting of a Population

種群非支配等級排序。

Why??不是說就為了找到非支配集合嗎? 這個不是多目標中優化中追求的一個goal?

解釋: 

Most evolutionary multi-objective optimization algorithms requires to find only the best non-dominated front in a population. These algorithms classify th population into two sets---the non-dominated set and the remaining dominated set.

However, the other algorihtms require to entire population to be classifed into various non-dominated levels.  

(1)Non-Dominated Sorting of a Population-------逐層的剔除一些非支配項,隨後對剩餘的種群找非支配集合,一次類推 

具中的例項:

 

 

在計算中: 複雜度有的時候會大於O(M*N*N)的計算量。 

(2) 不同的方法,給種群進行非支配等級排序 

Figure 14 種群中的Si以及ni
個體 支配個體 Si 被支配個體 ni的值
1 支配2 S1={2} 3,5 被3,5支配故  n1 = 2
2 1,3,4,5 4
3 1,2,4 {1,2,4} 0
4 2 {2} 3,5 2
5 1,2,4 {1,2,4} 0