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Lecture 10

# Step 2 for a soluon j p but j i check if soluon j

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Unformatted text preview: the previous O(MN2) algorithm) •  Remove them from popula/on •  Iden/fy the next ­best non ­dominated set in the popula/on •  Con/nue the process /ll all individuals in the popula/on are classiﬁed (sorted) •  O(MN3) computa/onal complexity 6 dominance b,d,c,e,f penalty(x) data a 5 d f(x) 10 15 Itera/on 1 data a b dominances 6 b,d,c,e,f e,f,c 5 c d e c f e penalty(x) Step 1 Set i = 1 and create an empty set P’. Step 2 For a solu/on j ∈ P (but j ≠ i), check if solu/on j dominates solu/on i. If yes, go to Step 4. Step 3 If more solu/ons are le^ in P, increment j by one and goto Step 2; otherwise, set P’= P’∪ {i}. Step 4 Increment i by one. If i ≤ N, go to Step 2; otherwise stop and declare P’ as the non ­ dominated set. O(MN2) computa/onal complexity, M is the number of objec/ves and N is the popula/on size. Examples a 4 b 3 2 e f 1 c d 0 0 5 f(x) 10...
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