Dr gafar zen alabdeen salh (2011) 1

Evolutionary Computation: Genetic algorithms

Can evolution be intelligent?

2Dr gafar zen alabdeen salh (2011)

evolutionary

computationgenetic algorithms

selection

(mutation)reproduction3Dr gafar zen alabdeen salh (2011)

Simulation of natural evolution

Charles Darwin

Mendal

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reproduction

, mutationcompetition

selection

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evoluation fitness

ecologymorphology

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How is a population with increasing fitness generated?

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Simulation of natural evolution

Genetic

Algorithms

GAs

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Genetic Algorithms

1 10 1 0 1 0 0 0 0 0 1 0 1 10

GA

crossovermutation

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GAsGA

encoding.

evaluation

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GAs

GA

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genetic algorithms

GAGA

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Basic genetic algorithms

Npc

crossover probabilitypm.

mutation probability

fitness function

N

x1, x2 , . . . , xN

f (x1), f (x2), . . . , f (xN) 13Dr gafar zen alabdeen salh (2011)

Basic genetic algorithms

–

N14Dr gafar zen alabdeen salh (2011)

Basic genetic algorithms

GA

generationGA

RUN

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GA

GA

GA

X

X

f(x) = 15 x – x2

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Genetic algorithms: case study

NPC

PM

PCPMGAs

Integer Binary code Integer Binary code Integer Binary code

1 11

2 7 12

3 8 13

4 9 14

5 10 15

6 1 0 1 1

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1

0 1 1 0

0 1 1 1

1 0 0 0

1 0 0 1

1 0 1 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

0 1 0 1

f(x) = 15 x – x2

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18Dr gafar zen alabdeen salh (2011)

The fitness function and chromosome locations

Chromosome

label

Chromosome

string

Decoded

integer

Chromosome

fitness

Fitness

ratio, %

X1 1 1 0 0 12 36 16.5

X2 0 1 0 0 4 44 20.2

X3 0 0 0 1 1 14 6.4

X4 1 1 1 0 14 14 6.4

X5 0 1 1 1 7 56 25.7

X6 1 0 0 1 9 54 24.8

x

50

40

30

20

60

10

00 5 10 15

f(x)

(a) Chromosome initial locations.

x

50

40

30

20

60

10

00 5 10 15

(b) Chromosome final locations.

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x5x6

x3x4

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Roulette wheel selection

Roulette wheel selection

100 0

36.743.149.5

75.2

X1: 16.5%

X2: 20.2%

X3: 6.4%

X4: 6.4%

X5: 25.3%

X6: 24.8%

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[0,100]

x6x2

x1x5

x2x5

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Crossover operatorbreak

x6x2

cloning

x2x5

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Crossover

X6i 1 00 0 01 0 X2i

0 01 0X2i 0 11 1 X5i

0X1i 0 11 1 X5i1 01 0

0 10 0

11 101 0

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25Dr gafar zen alabdeen salh (2011)

Mutation operator

Mutation

0 11 1X5'i 01 0

X6'i 1 00

0 01 0X2'i 0 1

0 0

0 1 111X5i

1 1 1 X1"i1 1

X2"i0 1 0

0X1'i 1 1 1

0 1 0X2i

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Mutation operator

x2

GAs

GA

Near-optimal

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The genetic algorithm cycle

1 01 0X1i

Generation i

0 01 0X2i

0 00 1X3i

1 11 0X4i

0 11 1X5i f = 56

1 00 1X6i f = 54

f = 36

f = 44

f = 14

f = 14

1 00 0X1i+1

Generation (i + 1)

0 01 1X2i+1

1 10 1X3i+1

0 01 0X4i+1

0 11 0X5i+1 f = 54

0 11 1X6i+1 f = 56

f = 56

f = 50

f = 44

f = 44

Crossover

X6i 1 00 0 01 0 X2i

0 01 0X2i 0 11 1 X5i

0X1i 0 11 1 X5i1 01 0

0 10 0

11 101 0

Mutation

0 11 1X5'i 01 0

X6'i 1 00

0 01 0X2'i 0 1

0 0

0 1 111X5i

1 1 1 X1"i1 1

X2"i0 1 0

0X1'i 1 1 1

0 1 0X2i

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The End