EE4047_Part6 - Part 6 Advantages City University of Hong...

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City University of Hong Kong Part 6: Advantages Strength of GA Handle multi-modal problems Handle multi-objective problems Parallelism Handle constrainted problems
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Multi-objective Problems Linear combination Nonlinear combination Pareto-based approach Pareto Optimality feasible searching domain Pareto Optimal Set Example: Minimization of f 1 and f 2 f 2 f 1
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Multi-objective Dominance : For an n-objective minimization problem, chromosome u is dominated by chromosome v ( v is preferable to u ) if f(v) is partially less than f(u) ( ) ( ) ( ) ( ) n j v f u f n i v f u f j j i i , , 2 , 1 and , , 2 , 1 L L = > = ( ) ( ) < u f v f p Example 5 3 3 2 x 2 5 4 3 2 x 1 f 4 ( · ) f 3 ( · ) f 2 ( · ) f 1 ( · ) Minimization Problem with 4-objectives x 1 is dominated by x 2 x 2 is more preferable than x 1
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Goldberg method All non-dominated individuals should have the same reproductive potential. A(1) D (1) C(1) B (1) E(2) F(2) G (3) f 1 f 2 Fonseca and Fleming Method The rank of each individual is defined by (1+p) where p is the number of individuals in the population that dominate it Non-dominated individuals are having the same rank, while dominated ones are penalized. A(1) D(1) C(1) B(1) E(2) F(3) G(4) f 1 f 2
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Goldberg vs Fonseca/Fleming In dividu al O bjective 1 O bjective 2 R an kin g F on cseca/ F lem in g R an kin g G oldberg 1 60.70(6) 90.68(2) 3 2 2 0.16(8) 26.76(4) 1 1 3 66.65(4) 15.94(5) 3 2 4 92.06(1) 90.76(1) 8 4 5 63.98(5) 0.38(8) 1 1 6 89.10(2) 9.59(6) 3 2 7 32.34(7) 4.89(7)
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