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# EE4047_Part5 - Part 5 Advantages City University of Hong...

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1 City University of Hong Kong City University of Hong Kong Part 5: Advantages Strength of GA square6 Handle multi-modal problems square6 Handle multi-objective problems square6 Parallelism square6 Handle constrainted problems

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2 Multi-objective Problems square6 Linear combination square6 Nonlinear combination square6 Pareto-based approach Pareto Optimality feasible searching domain Pareto Optimal Set Example: Minimization of f 1 and f 2 f 2 f 1
3 Multi-objective square6 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 ( · ) square6 Minimization Problem with 4-objectives square6 x 1 is dominated by x 2 square6 x 2 is more preferable than x 1

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4 A(1) D (1) C(1) B (1) E(2) F(2) G (3) f 1 f 2 Goldberg method square6 All non-dominated individuals should have the same reproductive potential. Fonseca and Fleming Method square6 The rank of each individual is defined by (1+p) where p is the number of individuals in the population that dominate it square6 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
5 Goldberg vs Fonseca/Fleming In divid u a l O bjective 1 O bjective 2 R a n k in g F o n cseca / F lem in g R an kin g G old berg 1 60.70(6) 90.68 (2) 3 2 2 0.16(8) 26.76 (4) 1 1

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• Spring '11
• XueQuan
• population Migration GA, Crossover Function Mutation, Function Mutation Evaluation, Mutation Evaluation Function

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EE4047_Part5 - Part 5 Advantages City University of Hong...

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