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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
create new string populations:
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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.
Procedures which are applied to successive string populations to
create new string populations:
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.
Procedures which are applied to successive string populations to
create new string populations:
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
GProcedures which are applied to successive string populations to
create new string populations:
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
GProcedures which are applied to successive string populations to
create new string populations:
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
GProcedures which are applied to successive string populations to
create new string populations:
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
GProcedures which are applied to successive string populations to
create new string populations:
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.
Procedures which are applied to successive string populations to
create new string populations:
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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
Measured and fitted values of milk activity
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
Measured and fitted values of milk activity
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
Measured and fitted values of milk activity
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.