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!
Selection
Individual A
Individual B
Individual C
Individual D
Individual E
Individual F
Individual G
Individual H
Recombination
Individual A
Individual A
Individual C
Individual E
Individual E
Individual F
Individual H
Individual H
Individual A
Individual H
Population
Individual A’
Individual B’
Individual C’
Individual D’
Individual E’
Individual F’
Individual G’
Individual H’
New Population
!
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1 1 1 1 1 1 1 1 1 1 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 1 1
Mutation
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0
Mutation Point
Mutation Point
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(0,1)
(3,0)
(6,0)
(1,1)
(4,0)
(9,0)
(5,0)
(8,0)
(2,1)
(7,0)
Second inversion
(0,1)
(2,1)
(8,0)
(5,0)
(9,0)
(4,0)
(1,1)
(6,0)
(3,0)
(7,0)
(0,1)
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Step 1: Building block identification.
All possible building blocks are generated and tested through selection.
0
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Step 2: Building block recombination.
Building blocks are recombined forming an optimal solution.
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Order 0 optimal template.
Order k optimal template.
mGA run detects order k+1 building blocks..
k = k+1;
If k < deception level
Else done, solved bounded deception of order k.
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Donating Chromosome
Recipient Chromosome
(1,1)
(4,0)
(4,1)
(2,1)
Grafting point
(5,1)
(2,1)
(3,1)
(1,0)
(3,0)
(5,0)
Material for transfer
(2,1)
(2,1)
(4,1)
(3,0)
(4,1)
(3,0)
(2,1)
(1,0)
(3,1)
(1,0)
(5,0)
(5,0)
Overfull Chromosome
Chromosome after duplicate deletion
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“…|k„j•c e ¥HkVe%g}ogx‰j%conSphlk„j!g n„ š ! couƒzA}‚cwgxe;k ! ‰!…|kmp|‰g1nm kyj!nSrth!p|k„ugip‹je c Oign„ kmp|aqk œ ‰!…|k„p|‰g;n„kƒj2nSrth!p|k„uƒgipAje_Kc Oig;n„ š £(`j0gxkS‰!…ª}ogi–Sg}n„ e%g}ogx‰j%conSpH¥ Qgh!gizPgxk„jnSrth0g Ntz|gih%couƒgipAj j%couƒgxei
£ g‡‹k„j!…tgihykx–dgihlk„‡Sgxe;k„jƒgxkd‰!… ‡Sgiptgihlk„j%conSp [nShƒsPnSj!… j!…tgp‹rtu;sPgihVn„(nSztj%couVk }strAc‚} adcopt‡
sA}wnt‰2¡e(k„p|aNj!…tgƒkx–dgihlk„‡Sg0}‚copt¡ k„‡dgƒ[nSh0j!…tn‹e%g;strAc‚}fadcwpt‡sA}wnt‰2¡ei£ “…tgƒz|ndztrA} kmj%conSp]e_Kc Oigxekmh!g1‰2…tn‹e%gip
} kmh!‡Sg(giptnSrt‡S…ªj!nƒk~–Sn„cfae%j!nt‰!…|kde%j%cf‰0g Hgx‰jlei£
Pcw‡drth!g ! £ # e%…tn Qej!…tg;– kmh%conSr|e(‰nSpA–Sgih!‡Sgip|‰g;zA}onSjle0kSe•j!…tgƒe%g}ogx‰j%conSp hlk„pt‡dgxe[h!nSu j2n š £
` ej!…tginSh%Kc Oigxa.¥•j!…tgqe%g}ogx‰j%conSp9hlkmj!gxeƒnm š ! k„p|a9k„s|n„–Sg{k } }e%…tn Q,k ‰nSpA–Sgih!‡Sgip|‰gXj!n j2…tg{‡„}onSs|k~}
œ
1
"s=2.0"
"s=1.9"
"s=1.8"
"s=1.7"
"s=1.6"
"s=1.5"
"s=1.4"
"s=1.3"
"s=1.2"
Convergence
0.8
0.6
0.4
selection = 1.2
0.2
0
0
10
20
30
40
50
60
70
80
Generation
! %
nSztj%cou;rtu{£ coj!…]kXe%g}ogx‰j%conSp hlk„j2g1nm š ¥ QgVe%gigyj!…tgƒnSztzPn‹e_coj!gS¥ j!…tgz|nSztrA}fk„j%conSp-‰ndp‹–Sgih2‡Sgxe(j!n
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€nSh‰gxen„˜‰h!nAe!e%n„–Sgihx£
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Œ Q…tgip]k}fk„h!‡dg[hlkS‰j*cwndp n„ j2…tg
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$
0.7
"s=2.0"
"s=1.9"
"s=1.8"
"s=1.7"
"s=1.6"
"s=1.5"
"s=1.4"
"s=1.3"
"s=1.2"
0.6
Linkage
0.5
0.4
0.3
selection = 1.2
0.2
0.1
0
0
10
20
30
40
50
60
70
80
Generation
!
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0Y =^.W.RHM ^HM
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#$
›
Gap y3
(4,1)
(2,1)
Gap y2
Gap y4
(3,1)
(1,1)
Gap y1
(5,1)
Gap y5
! •I I &
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0.58
0.56
Linkage
0.54
0.52
0.5
0.48
0.46
0.44
0.42
0.4
0
5
10
15
20
25
30
35
40
45
50
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"#
4000
"Theoretical"
"Empirical"
3500
Number of Individuals
3000
2500
2000
1500
1000
500
0
0
1
2
3
4
5
6
7
8
Problem Order
! + 1
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Donating Chromosome
Recipient Chromosome
(1,1)
(1,0)
(1,1)
(0,1)
Grafting point
(0,0)
(0,1)
(1,0)
(0,0)
Material for transfer
Grafting point = new point of interpretation
(1,1)
(0,1)
(0,1)
(1,1)
(0,1)
(1,0)
(0,0)
(0,0)
(1,0)
Overfull Chromosome
Chromosome after duplicate deletion
! 1
)+
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1
"Linkage"
"Convergence"
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
20
30
40
50
60
70
80
90
100
Generation
! 1 1
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0.8
0.75
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0.65
0.6
0.55
0.5
0.45
0
10
20
30
40
50
60
70
80
90
100
Generation
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1
0.9
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0.8
0.7
0.6
0.5
0.4
0
5
10
15
20
25
30
35
40
45
50
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1
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0.9
Linkage
0.8
0.7
0.6
0.5
0.4
0
10
20
30
40
50
60
70
80
90
100
Generation
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Donating Chromosome
Recipient Chromosome
(0,1)
(0,1)
PI
Grafting point
(0,1)
(0,0)
PI
(0,0)
(0,0)
Material for transfer
Grafting point = new point of interpretation (PI)
PI
(0,1)
PI
(0,1)
(0,0)
(0,1)
(0,0)
(0,0)
(0,0)
(0,0)
Overfull Chromosome
Chromosome after the deletion phase
!
# 1
+ œ
1
"s=2.5"
"s=3.0"
"s=3.5"
"s=4.0"
"s=4.5"
"s=5.0"
"s=5.5"
"s=6.0"
"s=6.5"
0.9
Linkage
0.8
0.7
0.6
0.5
0.4
0
10
20
30
40
50
60
70
80
Generation
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6
Fitness
5
4
3
2
1
0
1
2
3
4
5
6
Number of 1s in Building Block
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gx†Sr|k~}‚}oŒXn„
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Original Point of Interpretation (P)
(1,0)
(0,1)
(0,0)
(1,0)
(2,1)
(3,0)
(0,0)
(3,0)
(3,1)
(2,0)
(2,0)
(1,1)
Possible Point of Interpretation (P’)
! , I I I I J
1
0.9
Linkage
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
20
40
60
80
100
120
140
160
180
200
Generation
! + + œdœ
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20
18
Building Blocks Solved
16
14
12
10
8
6
4
2
0
20
40
60
80
100
120
140
160
180
Population Size
! " I J oJ I 1000
900
800
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700
600
500
400
300
200
100
0
0
50
100
150
200
250
300
350
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0.9
0.8
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0.6
0.5
0.4
0.3
0
50
100
150
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300
350
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›"
260
240
Population Size
220
200
180
160
140
120
5
10
15
20
25
30
35
40
Selection Rate
! 1
!I I & 1
I
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›"!
140
Population Size
120
100
80
60
40
20
0
5
10
15
20
25
30
35
40
Problem Size
! 1
1
I ' I 5
4.5
Log(Population Size)
4
3.5
3
2.5
2
1.5
1.5
2
2.5
3
3.5
4
Log(Problem Size)
! % 1
J  ’ ›
120
100
Generations
80
60
40
20
0
5
10
15
20
25
30
35
40
Problem Size
! I 1
1
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›"#
120
100
Generations
80
60
40
20
0
1.5
2
2.5
3
3.5
4
Log(Problem Size)
! I " 1
 }wp ’ oJ
4
Fitness
3
2
1
0
1
2
Number of 1s in Building Block
3
! !I + ›"
4
200
Population Size
180
160
140
120
100
80
4
6
8
10
12
14
16
Selection Rate
! 2 !I + !I J ' 2 J 900
800
Population Size
700
600
500
400
300
200
100
0
2
4
6
8
10
12
14
16
Problem Size
! J !I + I
I 1
J I ›œ
7
Log(Population Size)
6.5
6
5.5
5
4.5
4
3.5
2
4
6
8
10
12
14
16
Problem Size
! oJ I 1
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 ’  š ’  š .’  -š ’
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F(**1****)
F(**0****)
0
vs.
1
(1) Determine The Competitors
(2) Random Variables Represent The Competitors
n
Good End
+1
p
n/2
1-p
Start
p
1-p
0
-1
Bad End
0
(4) Setup The Parameters Of The Random Walk
(3) A Decision Variable Determines Transition Probabilities
! # 1 š «gxk„h!hlkmpt‡„copt‡ƒj!gih!uVe•k„‡‹k~copH¥
 š .’  ’
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 ’ šš š
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 š Aœ
% BBs correct
1
0.9
0.8
0.7
0.6
0
20
40
60
80
Population Size
100
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