Genetic Algorithem (Gordana Pantelic)

8/7/2019 Genetic Algorithem (Gordana Pantelic)

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Gordana PanteliGordana Panteli

Serbian Institute of Occupational Health Dr Dragomir Karajovi

EURADOS, Prague, WG3 Meeting, 10th February 2011


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GA -Optimization method which doesnt require the definitions ofinitial conditions.

Involve only - random number generation,

- string copies and

- partial string exchanges.

-are search algorithms based on the mechanics

of natural selection and natural genetic.

-GA have been developed by John Holland, hiscolleagues and his students at the Univesity of

Michigan, 1962.


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Population group of possible solutions of the problem.

A chromosome is represented by a string of finite lenght,

which could be the possible solution of the problem.

Lenght of chromosome number of parameters in the model.

An element in the string (gene) has the value of the

corresponding model parameter.

Parameter values

binary encoding,

real number.

a b c d1 111 e f g 111


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Parameters ai are randomly generated in the initial population

raaaa iiii += )( 1211. 1 b1 c1 d1 ... u12. 2 b2 c2 d2 ... u23. 3 b3 c3 d3 ... u34. 4 b4 c4 d4 ... u4... ..................

n. n bn cn dn ... unPo

pula

tion

G

1 10 100 1000 10000 100000 1000000

1000

10000

100000

1000000

1E7

5 populacija

10 populacija

20 populacija

vre

dnostkriterijumskef

unkcije

broj generacijaNumber of generation

5 Population

10 Population

20 Population


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Each chromosome in the population has

fitness function (sum of squareddifferences between the fit and

experimental data)

2

1

))(( tfAS i

n

i

i=

=

G


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Procedures which are applied to successive string populations to

create new string populations:

selection,

parent choosing,

crossover

mutation.

G


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selection,

parent choosing,

crossover

mutation.

a b c d1 111 e f g 111

a b c d2222

e f g222

Simple crossover

) 1-point crossover

GProcedures which are applied to successive string populations to



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a b c d1 111 e f g 111

a b c d2222

e f g222

G

selection,

parent choosing,

crossover

mutation.



Simple crossover

) 1-point crossover


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a b c d1 111

e f g 111a b c d 2222

e f g222

G

selection,

parent choosing,

crossover

mutation.



Simple crossover

) 1-point crossover


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a b c d e f g

a b c d e f g1 111111

2222222



selection,

parent choosing,

crossover

mutation.

Simple crossover

B) 2-point crossover


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a b c d e f g

a b c d e f g1 112222

2211112



selection,

parent choosing,

crossover

mutation.

Simple crossover

B) 2-point crossover


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a b c d e f g

a b c d e f g1 111111

2222222



selection,

parent choosing,

crossover

mutation.

Uniform crossover Form 2 offspring

where for each position in the offspring it

is decided with certain probability which

parent will contribute to its value.

G


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a

b c

d

e

f g

a

b c

d

e

f g1 11

1

1

11 22

2

2

22

2



selection,

parent choosing,

crossover

mutation.

Uniform crossover Form 2 offspring

where for each position in the offspring it

is decided with certain probability which

parent will contribute to its value.

G


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The primary role of the mutation is to

keep diversity in the population.

The mutation ought to create small

changes in the individuals from the

population.

p=0.01

G

selection,

parent choosing,

crossover

mutation.




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Two comparment model for predicting the

transport of radionuclides from pasture to milkt

t Adt

dA1=

mttt

m

AAIfdt

dA2=

ef +=1

bf +=2

t

tot eAA1=

ttottttottmom eAIfeAIfAA

12

2121

+=Pulse input

Solutions:

+

= )(1)(

1221

2

1

21

2

2112

ttttttotm eeIIfeeAIfA

Pulse and continuous input

Chernobyl accident


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Gross beta activity in

the erosolin Belgrade,

spring 1986

Gross beta activity in

thefall-outin Belgrade,spring 1986

Chernobyl accident


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PKB AgriculturalPlant in Belgrade

300

II group

Sampling from 14th May to25th May 1986 every day

+ 16th May 1986

40 kg fresh

green mass

I group

20 kg fresh

green mass

20 kg hay

Control group

40 kg hay (from 1985)

Experiment at PKB

G


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G

Experimental data:

Activity in milk

Unknown parameters:

ttottttottmom e

AIfe

AIfAA 12

2121

+=

+

= )(1)( 1221

2

1

21

2

2112

ttttttotm ee

IIfee

AIfA
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Gen fitness a1

a2

a3

a4

a5

1 59378.64 36.31 0.3245 906.11 0.5633 0.00847962 59378.64 36.31 0.3245 906.11 0.5633 0.0084796

3 59378.64 36.31 0.3245 906.11 0.5633 0.0084796

4 27710.73 36.31 0.2875 906.11 0.7461 0.0084796

5 27710.73 36.31 0.2875 906.11 0.7461 0.0084796

.

49 7698.80 56.74 0.2636 883.34 0.7950 0.0060037

62 7361.38 47.10 0.2636 883.34 0.7950 0.0060037..

495 3019.77 21.75 0.2069 854.67 0.6522 0.0051340

496 2671.49 21.75 0.2069 854.67 0.5941 0.0051340

..

22249 2427.83 1.00 0.1528 850.00 0.5391 0.0043700

22278 2426.24 1.00 0.1528 850.00 0.5367 0.0043700

..

2860917 12.34 1.00 0.2036 1087.82 0.3781 0.0029971

2924902 12.30 1.00 0.2038 1087.78 0.3778 0.002997


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Measured and fitted values of milk activity

131I

Experiment at PKB

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160I grupa

II grupa

Kontrolna

FIT (I grupa)

FIT (II grupa)

FIT (Kontrolna)

Aktivnost(B

q/l)

dani

I group

II group

Control

FIT (I group)

FIT (II group)

FIT (Control)

days

Activity


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134Cs

137Cs

Experiment at PKB


0 5 10 15 20 25 30 35

0

2

4

6

8

10

12I grupa

II grupa

Kontrolna

FIT (I grupa)

FIT (II grupa)FIT (Kontrolna)

Aktivnost(Bq/l)

dani

I group

II group

Control

FIT (I group)

FIT (II group)FIT (Control)

days

Activity

0 5 10 15 20 25 30 350

5

10

15

20

25

dani

I grupa

II grupa

Kontrolna

FIT (I grupa)FIT (II grupa)

FIT (Kontrolna)

Aktivnost(Bq/l)

I group

II group

Control

FIT (I group)FIT (II group)

FIT (Control)

Activity

days


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103Ru

106Ru

Experiment at PKB


0 5 10 15 20 25 30 350

5

10

15

20

25I grupa

II grupa

Kontrolna

FIT (I grupa)

FIT (II grupa)FIT (Kontrolna)

Aktivnost(Bq/l)

dani

I group

II group

Control

FIT (I group)

FIT (II group)FIT (Control)

days

Activity

0 5 10 15 20 25 30 350

5

10

15

20 I grupa

II grupa

Kontrolna

FIT (I grupa)FIT (II grupa)

FIT (Kontrolna)

Aktivnost(Bq/l)

dani

I group

II group

Control

FIT (I group)

FIT (II group)

FIT (Control)

Activity

days


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Activity in food 14thMay 1986 in experiment at PKB (Bq/kg)

Radionuclide Control I group II group

131I 127

133

1068

962

2009

1880

134

Cs 2229.2

284240

546562

137Cs 49

55.6

724

657

1399

1180

103Ru 153

180

1842

2051

3531

3171

106Ru 97

111

629

647

1161

1340

X measured, X calculated


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Activity in milk 14thMay 1986 in experiment at PKB (Bq/l)

Radionuclide Control I group II group

131I 15.4

13

44.8

41.4

57.8

52.4

134

Cs 0.240.2

3.22.7

32.9

137Cs 3.9

3.3

5.7

5.3

7.5

6.7

103Ru 21

22.3

16.1

17.5

19.4

19.3

106Ru 9

8.2

10

10.1

11.9

14

X measured, X calculated


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106Ru

106Ru

0 5 10 15 20 25 30 350

5

10

15

20 I grupa

II grupa

Kontrolna

FIT (I grupa)

FIT (II grupa)

FIT (Kontrolna)

Aktivnost(

Bq/l)

dani

0 5 10 15 20 25 30 350

5

10

15

20I grupa

II grupa

Kontrolna

FIT (I grupa)

FIT (II grupa)

FIT (Kontrolna)

Aktivnost(B

q/l)

dani


Pulse input

Experiment at PKB

Pulse and continuous input

I group

II group

Control

FIT (I group)

FIT (II group)

FIT (Control)

Activity

days I groupII group

Control

FIT (I group)

FIT (II group)

FIT (Control)

Activity

days


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Nuclide

Obtain with GA Literature data

(IAEA TRS 472, 2010)

Pulse input Pulse and

continuous input

Average

values

Range

131I (1.20 0.15) .10-3 (1.15 0.09) .10-3 5.4.10-3 4.10-4 - 2.5.10-2

134Cs (4.9 2.8) .10-4 (4.4 1.8) .10-4

137Cs (4.3 0.9) .10-4 (3.2 0.9) .10-4

4.6.10-3 6.10-4 - 6.8.10-2

103Ru (3 1) .10-4 (4.2 1.6) .10-4

106Ru (4.3 2.0) .10-4 (7.3 0.8) .10-4

9.4.10-6 6.7.10-7 - 1.4.10-4

Radionuclide transfer coefficient to milk

(day/l )

Biological half-life of radionuclides in milk


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Nuclide

Experiment

1/2(day)

Group Pulse input Pulse andcont.input

Literature data

1/2(day) /Reference/

131I

I

II

Control

4.1

3.2

6.0

4.3

3.9

7.9

3.0 /Shaeffer, 1981/

1.4 /Bonka et al., 1989/

0.87-2.57 /Vandecasteele et al., 2000

134Cs

I

II

Control

1.5

1.1

3.1

2.8

2.8

3.7

137Cs

I

II

Control

1.1

1.1

3.5

1.9

2.8

3.5

4 /Van den Hoek et al., 1969/

4 /Karlen, 1993/

1.5 /Voigt et al., 1989/

103Ru

I

II

Control

0.7

0.7

1.1

0.9

0.8

1.8

106Ru III

Control

0.70.7

2.6

1.20.7

2.2


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Parameter uncertainty < 10 %

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

II grupa

FIT (1. put)

FIT (2. put)

FIT (3. put)

Aktivnost(Bq/l)

dani

0 5 10 15 20 25 30 350

5

10

15

20

25 II grupa

FIT (1. put)

FIT (2. put)

FIT (3. put)

Aktivnost(Bq/l)

dani

131I

137Cs

Uncertainty

0.6-8.8 %

Uncertainty

1.2 - 5 %


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GA - Optimization method that imitate natural selection

mechanisms.

It doesnt require the definitions of initial conditions.Involve only random number generation, string copies andpartial

string exchanges.

Advantage ofGA in solving optimization problem easy to apply

and easy to find appropriate parameters.

GA opearates with populations, other metods deals with

individuals.

Results for transfer coefficients and biological half life agree with

literature data.


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Thank you for your attention.

Documents

Genetic Algorithem (Gordana Pantelic)