Машинное обучение 1, осень 2015: Генетические алгоритмы

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• . , .

, 2015

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• 1 2 3 Differential evolution4 No free lunch theorem

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• F0 = arg maxF

p(F |X )

+ ;

F; .

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• dream team; ; .

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• . "" , "": .

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• 1 2 ""3

1 2

3 ""4 ""

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• - / - - - "" "" - "" -

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• 1 2 ""3

1 2

3 ""4 ""

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• . :

[0, 1]n {0, 1}k

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• - ! :

, "" shuffle"" "" ( ) :)

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• , . !

"" :

n-point crossover;cutnsplice; .

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• rossover

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• Cut and splice

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• (genetic drift) . MCMC/ .

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• vs

- "" , - "". :

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• % "" "penalty"

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• pros cons , .:

( :));

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:

;

( );

.

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• Differential Evolution

arg maxRn

F ()

1 2 ,

x P :1 a, b, c P ;2 k U(1..n);3 y = (yi) i

1 r U((0, 1))

2 yi =

{ai + F (bi ci ), i = k |r < Cyi = xi

4 , .3

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• 2 . ? :: : , :

Theorem (No free lunch theorem)

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• NFL:

dm = {(d xm(1), d ym(1)), . . . , (d xm(m), d ym(m))}f : X YF = YX

p(f ) = 1F

Theorem (David Wolpert and William G.Macready (1997)) a1 a2:

f p(dym|f ,m, a1) =

f p(d

ym|f ,m, a2)

f p(dym|f0,M ,m, a1) =

f p(d

ym|f0,M ,m, a2)

. , . , -, 2015 . 21 22

• NFL:

:) ,

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No free lunch theorem

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