4. Nontraditional
Optimization Algorithms
Scientists have tried to mimic the nature
throughout the history.
Nature
Manmade
Nature
Manmade
Crane (bird)
Crane (Machine)
Nature
Manmade
Crane (bird)
Crane (Machine)
Fish
Submarine
Nature
Manmade
Crane (bird)
Crane (Machine)
Fish
Submarine
bird
Aircraft
Nature
Manmade
Crane (bird)
Crane (Machine)
Fish
Submarine
bird
Aircraft
Brain processes
Microprocessor
Nature
Manmade
Crane (bird)
Crane (Machine)
Fish
Submarine
bird
Aircraft
Brain processes
Microprocessor
Biological neural
networks
Artificial Neural
networks
Nature
Manmade
Crane (bird)
Crane (Machine)
Fish
Submarine
bird
Aircraft
Brain processes
Microprocessor
Biological neural
networks
Artificial Neural
networks
Reproduction
process
Genetic
Algorithms
The nontraditional optimization algorithms
are
The nontraditional optimization algorithms
are
Genetic Algorithms
The nontraditional optimization algorithms
are
Genetic Algorithms
Neural Networks
The nontraditional optimization algorithms
are
Genetic Algorithms
Neural Networks
Ant Algorithms
The nontraditional optimization algorithms
are
Genetic Algorithms
Neural Networks
Ant Algorithms
Simulated Annealing
4.1 Genetic Algorithms
4.1 Genetic Algorithms
4.1.(a) Notion of Genetic Algorithms
4.1 Genetic Algorithms
4.1.(a) Notion of Genetic Algorithms
Human
4.1 Genetic Algorithms
4.1.(a) Notion of Genetic Algorithms
Human
1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0
4.1 Genetic Algorithms
4.1.(a) Notion of Genetic Algorithms
Human
1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0
23 chromosomes
4.1 Genetic Algorithms
4.1.(a) Notion of Genetic Algorithms
Human
1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0
23 chromosomes
A fetus is formed by a Male(sperm) and female(egg).
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
Crossover point
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 0 0 1 1 0
0 1 1 1 1 0 0 1
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 0 0 1 1 0
0 1 1 1 1 0 0 1
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 0 0 1 1 0
0 1 1 1 1 0 0 1
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 0 0 1 1 0
1 1 1 1 0 0 0 0
0 1 1 1 1 0 0 1
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 1 1 0 0 1
+
0 1 1 0 0 1 1 0
1 0 1 0 0 1 1 0
1 1 1 1 0 0 0 0
0 1 1 1 1 0 0 1
0 0 1 0 1 1 1 1
4.1.(b) Some Basic Facts
4.1.(b) Some Basic Facts
Powerful
4.1.(b) Some Basic Facts
Powerful, wealthy
4.1.(b) Some Basic Facts
Powerful, wealthy, smart
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people get more dating opportunities.
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people get more dating opportunities.
But, it is random.
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people get more dating opportunities.
But, it is random. (Probability of SelectionFitness)
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people get more dating opportunities.
But, it is random.
A kid may be more mother like or father like.
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people get more dating opportunities.
But, it is random.
A kid may be more mother like or father like.
But, it is random.
4.1.(b) Some Basic Facts
Powerful, wealthy, smart, good looking, Educated or
caring people get more dating opportunities.
But, it is random.
A kid may be more mother like or father like.
But, it is random. (Crossover Point)
Approximately 10% of couples do not have kids since
either they opt not to have them or
Approximately 10% of couples do not have kids since
either they opt not to have them or they cannot have
them biologically.
Approximately 10% of couples do not have kids since
either they opt not to have them or they cannot have
them biologically.
But, it is random.
Approximately 10% of couples do not have kids since
either they opt not to have them or they cannot have
them biologically.
But, it is random.
The population can be maintained at a constant level
by perfect family planning.
Approximately 10% of couples do not have kids since
either they opt not to have them or they cannot have
them biologically.
But, it is random.
The population can be maintained at a constant level
by perfect family planning.
It is done by limiting 2 kids per family.
The evolutionary process can be expedited by
improving the variety of the gene pool.
The evolutionary process can be expedited by
improving the variety of the gene pool.
It is done via mutation.
The evolutionary process can be expedited by
improving the variety of the gene pool.
It is done via mutation.
Mutation Process
The evolutionary process can be expedited by
improving the variety of the gene pool.
It is done via mutation.
Mutation Process
1 0 1 1 1 0 0 1
The evolutionary process can be expedited by
improving the variety of the gene pool.
It is done via mutation.
Mutation Process
1 0 1 1 1 0 0 1
1 0 0 1 1 0 0 1
Genetic algorithms are usually applied for
maximization problems.
Genetic algorithms are usually applied for
maximization problems.
To minimize f(x) (f(x)>0)using GAs, consider
Genetic algorithms are usually applied for
maximization problems.
To minimize f(x) (f(x)>0)using GAs, consider
maximization of
Genetic algorithms are usually applied for
maximization problems.
To minimize f(x) (f(x)>0)using GAs, consider
maximization of
1
1+f(x)
4.1.(c) Example
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
0
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
4
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
4
6
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
4
6
8
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
4
6
8
10
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
4
6
8
10
12
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101100
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101100
(12,0)
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101100
(12,0)=110000
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101100
(12,0)=110000
(8,6)
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101100
(12,0)=110000
(8,6)=100110
0
2
4
6
8
10
12
14
x
4.1.(c) Example
Maximize y1.3+10e^(-xy)+sin (x-y)+3 in R=[0,14]×[0,7].
y
(0,5)=000101
(2,7)=001111
7
(6,1)=011001
(10,4)=101100
(12,0)=110000
(8,6)=100110
0
2
4
6
8
10
12
14
x
String
000101
001111
011001
101100
110000
100110
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Fitness:
21.02
21.02+15.46+4.11+9.17+13.21+13.31
= 0.276
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
Fitness:
21.02
21.02+15.46+4.11+9.17+13.21+13.31
= 0.276
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
Fitness:
15.46
21.02+15.46+4.11+9.17+13.21+13.31
= 0.203
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
Fitness:
4.11
21.02+15.46+4.11+9.17+13.21+13.31
= 0.054
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
String
0.276
0.479
0.533
0.653
0.826
1.000
0.269
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
String
0.276
0.479
0.533
0.653
0.826
1.000
0.269
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
0.923
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
0.923
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
0.117
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
0.117
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
0.366
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
0.366
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
0.804
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
0.804
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
0.589
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
0.589
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
String
000101
100110
000101
001111
110000
101100
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
0.720-0.899
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
0.540-0.719
Cum.Prob
0.360-0.539
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
0.180-0.359
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
0.000-0.179
String
000101
100110
000101
001111
110000
101100
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
0.707
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
0.508
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
0.240
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000101
100110
000101
001111
110000
101100
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000110
100101
000111
001101
111100
100000
String
000101
100110
000101
001111
110000
101100
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000110
100101
000111
001101
111100
100000
String
000101
100110
000101
001111
110000
101100
Changes if
p>0.95
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000110
100101
000111
001101
111100
100000
String
000101
100110
000101
001111
110000
101100
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000110
001101
000111
001101
111100
110000
String
000101
100110
000101
001111
110000
101100
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000110
001101
000111
001101
111100
110000
String
000101
100110
000101
001111
110000
101100
Go to iter. 2
String
000101
100110
000101
001111
110000
101100
String
000110
100101
000111
001101
111100
100000
Prob.
0.276
0.203
0.054
0.120
0.173
0.174
Mutation
f(x,y)
21.02
15.46
4.11
9.17
13.21
13.31
Crossover
String (x,y)
000101 (0,5)
001111 (2,7)
011001 (6,1)
101100 (10,4)
110000 (12,0)
100110 (8,6)
Cum.Prob
0.276
0.479
0.533
0.653
0.826
1.000
String
000110
001101
000111
001101
111100
110000
String
000101
100110
000101
001111
110000
101100
Go to iter. 2
String
000110
001101
000111
001101
111100
110000
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
23.17
11.05
25.43
11.05
9.24
13.21
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
23.17
11.05
25.43
11.05
9.24
13.21
Continue
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
23.17
11.05
25.43
11.05
9.24
13.21
Continue
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
23.17
11.05
25.43
11.05
9.24
13.21
Previous Avg. = 12.71
New Avg. = 15.52
Continue
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
23.17
11.05
25.43
11.05
9.24
13.21
Continue
Previous Avg. = 12.71
Previous Max. = 21.02
New Avg. = 15.52
New Max. = 25.43
String (x,y)
000110 (0,6)
001101 (2,5)
000111 (0,7)
001101 (2,5)
111100 (14,4)
110000 (12,0)
f(x,y)
23.17
11.05
25.43
11.05
9.24
13.21
Continue
Previous Avg. = 12.71
Previous Max. = 21.02
New Avg. = 15.52
New Max. = 25.43
Previous =
New =
y
7
0
2
4
6
8
10
12
14
x
Previous =
New =
y
7
0
2
4
6
8
10
12
14
x
4.2 Neural Networks
4.2 Neural Networks
(a) Biological Neural Networks
4.2 Neural Networks
(a) Biological Neural Networks
4.2 Neural Networks
(a) Biological Neural Networks
4.2 Neural Networks
(a) Biological Neural Networks
Neurons
Axon
Axon
Nucleus
Axon
Nucleus
Axon
dendrites
Nucleus
Axon
dendrites
Nucleus
Axon
dendrites
Nucleus
Axon
dendrites
Nucleus
Axon
dendrites
Nucleus
Axon
Synapses
dendrites
Nucleus
Axon
Synapses
dendrites
Nucleus
Axon
Synapses
Neuron
dendrites
Nucleus
Axon
Synapses
Neuron
dendrites
Nucleus
Axon
Synapses
Neuron
The gap changes
while information
are being stored.
A neuron is multi-input and single-output
object..
A neuron is multi-input and single-output
object..
A nucleus produces a signal and passes it
through the axon when it is excited by the
signals received from other neurons..
A neuron is multi-input and single-output
object..
A nucleus produces a signal and passes it
through the axon when it is excited by the
signals received from other neurons..
If the signal is large enough to pass through
synapse, the dendrites carry it to the adjacent
neurons.
(b) Architecture of Artificial Neural Networks
(b) Architecture of Artificial Neural Networks
The subsections are
(b) Architecture of Artificial Neural Networks
The subsections are
Simple model of a neuron
(b) Architecture of Artificial Neural Networks
The subsections are
Simple model of a neuron
Neuron transfer function (characteristics)
(b) Architecture of Artificial Neural Networks
The subsections are
Simple model of a neuron
Neuron transfer function (characteristics)
Weights between two neurons
(b) Architecture of Artificial Neural Networks
The subsections are
Simple model of a neuron
Neuron transfer function (characteristics)
Weights between two neurons
The complete model
(i) Simple Model of a Neuron
+
axon
dendrites
Synapses
cell body
(ii) Transfer Function of a Neuron
(ii) Transfer Function of a Neuron
linear
(ii) Transfer Function of a Neuron
linear
threshold
(ii) Transfer Function of a Neuron
linear
threshold
sigmoid
(iii) Weights between Two Neurons
(iii) Weights between Two Neurons
(iii) Weights between Two Neurons
The signal attenuation is modeled by a multiplier
m(0≤m≤1).
(iii) Weights between Two Neurons
The signal attenuation is modeled by a multiplier
m(0≤m≤1).
m
(iii) Weights between Two Neurons
The signal attenuation is modeled by a multiplier
m(0≤m≤1).
m
0≤m≤1
(iii) Weights between Two Neurons
The signal attenuation is modeled by a multiplier
m(0≤m≤1).
m
m may be assigned real values.
0≤m≤1
(iv) Complete Model
(iv) Complete Model
(iv) Complete Model
(iv) Complete Model
(iv) Complete Model
(iv) Complete Model
(iv) Complete Model
Input layer
Hidden layer(s)
(iv) Complete Model
Input layer
Hidden layer(s)
(iv) Complete Model
Input layer
Output layer
u1
u2
uk
un
m1
m2
mk
mn
v
u1
u2
uk
un
m1
m2
mk
mn
v
u1
u2
uk
un
m1
m2
v
mk
mn
v=f(Σmiui+θ)
u1
u2
uk
m1
m2
v
mk
un
mn
v=f(Σmiui+θ)
θ-threshold level
u1
u2
uk
un
m1
m2
v
mk
mn
v=f(Σmiui+θ)
θ-threshold level, f-linear
u1
u2
uk
un
m1
m2
v
mk
mn
v=f(Σmiui+θ)
θ-threshold level, f-linear, threshold
u1
u2
uk
un
m1
m2
v
mk
mn
v=f(Σmiui+θ)
θ-threshold level, f-linear, threshold or sigmoid
u1
u2
uk
un
m1
m2
v
mk
mn
v=f(Σmiui+θ)
θ-threshold level, f-linear, threshold or sigmoid
m’s are changed while information are being stored.
(c) Special Types of Networks
Hidden layer(s)
Feed forward networks
Input layer
Output layer
Hidden layer(s)
Feedback networks
Input layer
Output layer
(d) Pattern Recognition
zero
one
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
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1
0
1
0
0
1
1
1
0
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1
1
1
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0
X21 X22 X23 o/p
0
0
0
0
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1
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1
0/1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
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1
X31 X32 X33 o/p
0
0
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0
0
1
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0
1
0/1
0/1
0
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1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
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0
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0
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1
1
1
0
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1
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1
0
1
0
0
1
1
X21 X22 X23 o/p
0
0
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0
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0
1
0/1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
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0
1
0
0
1
1
1
0
0
1
0
1
1
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1
0
1
0
0
1
1
0
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
X31 X32 X33 o/p
0
0
0
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0
1
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
0
0
1
1
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0
0
1
0
1
1
1
1
1
0
1
X21 X22 X23 o/p
0
0
1
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1
0
1
0/1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
X31 X32 X33 o/p
0
0
0
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1
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0
1
1
1
0
0
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0
1
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1
0
1
X31 X32 X33 o/p
0
0
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0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0/1
0
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0
1
1
1
0
0
1
0
1
0/1
1
1
1
1
0
1
0
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0
1
1
1
0
0
1
0
1
0/1
0/1
0
1
1
1
1
0
1
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0/1
1
1
1
1
0
1
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0/1
1
1
1
1
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0/1
1
1
1
1
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
1
0
1
0
1
0/1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0/1
0/1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0/1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
Pause
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
Pause
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
X11 X12 X13 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
X21 X22 X23 o/p
X31 X32 X33 o/p
0
0
0
0
0
0
1
1
0
1
0
1
1
0/1
1
0/1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0/1
0
0/1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
(e) System identification and modeling
(e) System identification and modeling
Modeling plantations (Agriculture)
(e) System identification and modeling
Modeling plantations (Agriculture)
Modeling earthquake dynamics (Structures)
(e) System identification and modeling
Modeling plantations (Agriculture)
Modeling earthquake dynamics (Structures)
Modeling channel disturbances (Communication)
(e) System identification and modeling
Modeling plantations (Agriculture)
Modeling earthquake dynamics (Structures)
Modeling channel disturbances (Communication)
Modeling crash resistance of automobiles (Auto Eng.)
SUPERVISOR
SUPERVISOR
Supervised learning
Minimization of error between expected and
computed output is obtained by adjusting
weights.
Minimization of error between expected and
computed output is obtained by adjusting
weights.
The supervisor decides the rule which is
applied to adjust weights.
Unsupervised learning
Minimization of error between expected and
computed output is obtained by adjusting
weights (as in supervised learning).
Minimization of error between expected and
computed output is obtained by adjusting
weights (as in supervised learning).
The rule is inbuilt.
Pause
Ground accel.
Movement
Ground accel.
Movement
10 sin 1000t
2.5
30 sin 1000t
3
10 sin 4000t
3
Ground accel.
Movement
10 sin 1000t
2.5
30 sin 1000t
3
10 sin 4000t
3
50 sin 3000t
?
Ground accel.
Movement
10 sin 1000t
2.5
30 sin 1000t
3
10 sin 4000t
3
50 sin 3000t
?
10→1, 1000→1
x
y
z
1
3
1
1
1
4
2.5
2.5
3
1
1
x
y
z
1
3
1
1
1
4
2.5
2.5
3
1
1
x
y
z
1
3
1
1
1
4
2.5
2.5
3
0.5
x
y
z
1
3
1
1
1
4
2.5
2.5
3
0.5
2
1
1
2
1
1
1
2
x
y
z
1
3
1
1
1
4
2.5
2.5
3
0.5
(1,0.5)
2
1
1
2
1
1
(1,0.5)
1
2
x
y
z
1
3
1
1
1
4
2.5
2.5
3
0.5
(1,0.5)
2
1
(1.5,1)
2
1
1
1
(1,0.5)
2
1
(1,0.5)
x
y
z
1
3
1
1
1
4
2.5
2.5
3
0.5
(1,0.5)
2
1
(1.5,1)
2
1
1
1
(1,0.5)
(3,2.5)
2.5
2
1
(1,0.5)
x
y
z
1
3
1
1
1
4
2.5
3
3
x
y
z
1
3
1
1
1
4
2.5
3
3
3
3
1
x
y
z
1
3
1
1
1
4
2.5
3
3
0.5
3
3
1
x
y
z
1
3
1
1
1
4
2.5
3
3
0.5
1
3
1
-1
1
3
1.25
1
5.6
x
y
z
1
3
1
1
1
4
2.5
3
3
0.5
(3,2.5)
1
3
1
-1
1
3
1.25
1
(1,0.5)
5.6
x
y
z
1
3
1
1
1
4
2.5
3
3
0.5
(3,2.5)
1
3
1
(3,2.5)
-1
1
3
1.25
1
(1,0.5)
5.6
(5.3,4.8)
x
y
z
1
3
1
1
1
4
2.5
3
3
0.5
(3,2.5)
1
3
1
(3,2.5)
-1 (3.5,3)
1
3
1.25
1
(1,0.5)
5.6
(5.3,4.8)
x
y
z
1
3
1
1
1
4
2.5
3
3
0.5
(1,0.5)
6.83
1
1
(6.92,6.42)
1
(3.5,3)
1
3
-6.6
4
(4,3.5)
0.127
(0.94,0.44)
x
y
z
1
3
1
1
1
4
2.5
2.5
2.5
0.5
(5,4.5)
6.83
5
1
(33.25,32.75)
1
(4.24,3.74)
1
2.5
-6.6
3
(3,2.5)
0.127
(4.82,4.32)
4.3 Ant Algorithms
4.3 Ant Algorithms
(a) Why are the ants special?
(a) Why are the ants special?
Strength
(a) Why are the ants special?
Strength
The strongest animal – the black ant can carry
50 times of its own weight
Pain of Sting
Pain of Sting
1.0 - Sweat bee:
Light, ephemeral,
almost fruity.
Pain of Sting
1.0 - Sweat bee:
Light, ephemeral,
almost fruity. A tiny
spark has singed a
single hair on your
arm.
Pain of Sting
1.0 - Sweat bee:
Light, ephemeral,
almost fruity. A tiny
spark has singed a
single hair on your
arm.
Pain of Sting
1.0 - Sweat bee:
Light, ephemeral,
almost fruity. A tiny
spark has singed a
single hair on your
arm.
4.0+ Bullet ant: Pure, intense, brilliant pain.
Pain of Sting
1.0 - Sweat bee:
Light, ephemeral,
almost fruity. A tiny
spark has singed a
single hair on your
arm.
4.0+ Bullet ant: Pure, intense, brilliant pain. Like
fire-walking over flaming charcoal with a 3-inch
rusty nail in your heel.
Queen’s Ability to Preserve Sperms
Queen’s Ability to Preserve Sperms
A queen can keep sperms stored in her for nearly
18-20 years.
Ant Colony
Ant Colony
A social insect. Their behavior is geared to the
survival of colony rather than that of individuals.
Ant Colony
A social insect. Their behavior is geared to the
survival of colony rather than that of individuals.
Colony – structure of organization is excellent
Individuals – very simple
Ant Colony
A social insect. Their behavior is geared to the
survival of colony rather than that of individuals.
Colony – structure of organization is excellent
Individuals – very simple
Colony – structure of organization is excellent
Individuals – very simple
How do they use pheromones?
How do they use pheromones?
Ants deposit pheromones while moving from nest
to food sources and vice versa.
How do they use pheromones?
Ants deposit pheromones while moving from nest
to food sources and vice versa.
This activity creates a pheromone trail.
How do they use pheromones?
Ants deposit pheromones while moving from nest
to food sources and vice versa.
This activity creates a pheromone trail.
Ants smell pheromones and while choosing a path
they choose the path with high pheromone density.
(b) Artificial Ants
(b) Artificial Ants
Similarities with Real Ants
(b) Artificial Ants
Similarities with Real Ants
Colony of cooperating ants
(b) Artificial Ants
Similarities with Real Ants
Colony of cooperating ants
Deposition of pheromone while moving
(b) Artificial Ants
Similarities with Real Ants
Colony of cooperating ants
Deposition of pheromone while moving
Shortest path searching and local moves
(b) Artificial Ants
Similarities with Real Ants
Colony of cooperating ants
Deposition of pheromone while moving
Shortest path searching and local moves
Stochastic and myopic state transition policy
Differences with Real Ants
Differences with Real Ants
An artificial ant has an internal state.
(the memory of past actions)
Differences with Real Ants
An artificial ant has an internal state.
(the memory of past actions)
The amount of pheromone deposited is
proportional to the quality of solution
obtained.
(c) Traveling Salesman Problem
(c) Traveling Salesman Problem
2
3
1
4
5
(c) Traveling Salesman Problem
2
3
1
4
5
(c) Traveling Salesman Problem
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
Ant decision table
8
2
4
6
3
1
3
3
5
9
5
4
8
5
7
1
2
3
4
5
1
2
3
4
5
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
2
3
4
5
1
2
3
4
5
Ant decision table
8
2
4
6
3
1
3
3
5
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
3
3
5
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.883
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.883
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.883
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.137
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.137
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.780
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.780
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.780
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.780
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.641
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.641
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.641
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
Total length = 36
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.25
0.25
0.25
0.25
2
3
0.25 0.50
0.50
0.50
0.50 0.75
0.50 0.75
4
5
0.75 1.00
0.75 1.00
0.75 1.00
1.00
1.00
Ant decision table
Total length = 36
8
2
4
3
1
Add 1/36 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
Total length = 36
8
2
4
3
1
Add 1/36 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.446
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.446
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.446
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.977
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.977
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.977
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.301
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.301
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.301
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.28
0.24
0.24
0.24
2
3
0.24 0.48
0.52
0.52
0.48 0.76
0.48 0.72
4
5
0.72 1.00
0.76 1.00
0.76 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.521
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.521
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.521
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.841
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.841
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.076
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.676
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.876
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.876
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
3
1
Random number
0.876
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
Total length = 25
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.26
0.22
0.30
0.22
2
3
0.22 0.54
0.48
0.48
0.52 0.78
0.54 0.74
4
5
0.74 1.00
0.78 1.00
0.70 1.00
1.00
1.00
Ant decision table
Total length = 25
8
2
4
3
1
Add 1/25 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
Total length = 25
8
2
4
3
1
Add 1/25 to
relevant
places
6
5
3
3
9
5
4
8
5
7
Next iteration…
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.27
0.19
0.35
0.19
2
3
0.19 0.61
0.46
0.42
0.59 0.81
0.56 0.73
4
5
0.77 1.00
0.81 1.00
0.61 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
Next iteration…
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
Total length = 25
8
2
4
6
3
1
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.29
0.21
0.29
0.21
2
3
0.21 0.57
0.50
0.46
0.55 0.79
0.52 0.71
4
5
0.75 1.00
0.79 1.00
0.67 1.00
1.00
1.00
Ant decision table
Total length = 25
8
2
4
3
1
Add 1/25 to
relevant
places
6
5
3
3
9
5
4
8
5
7
1
1
2
3
4
5
0.35
0.19
0.27
0.19
2
3
0.19 0.61
0.54
0.42
0.59 0.81
0.48 0.65
4
5
0.77 1.00
0.81 1.00
0.61 1.00
1.00
1.00
Ant decision table
Total length = 25
8
2
4
3
1
Add 1/25 to
relevant
places
6
5
3
3
9
5
4
8
5
7
Next iteration…
1
1
2
3
4
5
0.33
0.17
0.33
0.17
2
3
0.17 0.65
0.50
0.38
0.63 0.83
0.52 0.67
4
5
0.79 1.00
0.83 1.00
0.55 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
After 7 iterations…
1
1
2
3
4
5
0.21
0.09
0.49
0.09
2
3
0.09 0.73
0.40
0.28
0.69 0.87
0.68 0.79
4
5
0.87 1.00
0.91 1.00
0.47 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
After another 10 iterations…
1
1
2
3
4
5
0.05
0.00
0.79
0.00
2
3
0.01 0.97
0.16
0.12
0.83 0.97
0.88 0.95
4
5
0.99 1.00
0.97 1.00
0.21 1.00
1.00
1.00
Ant decision table
Total length = 22
8
2
4
3
1
Add 1/22 to
relevant
places
6
5
3
3
9
5
4
8
5
7
(d) Other Applications
(d) Other Applications
Job-shop scheduling problem
(d) Other Applications
Job-shop scheduling problem
Given M machines and a sequence of J jobs, it is
required assign operations and time intervals to so
that the completion time is minimum.
(d) Other Applications
Job-shop scheduling problem
Given M machines and a sequence of J jobs, it is
required assign operations and time intervals to so
that the completion time is minimum.
Quadratic Assignment problem
(d) Other Applications
Job-shop scheduling problem
Given M machines and a sequence of J jobs, it is
required assign operations and time intervals to so
that the completion time is minimum.
Quadratic Assignment problem
Assigning N facilities to N locations so that the cost
of assignment is minimized.
Graph coloring problem
Graph coloring problem
Coloring a graph with minimum number of colors.
Graph coloring problem
Coloring a graph with minimum number of colors.
Vehicle routine problem
Graph coloring problem
Coloring a graph with minimum number of colors.
Vehicle routine problem
To find the minimum cost vehicle routine so that
Graph coloring problem
Coloring a graph with minimum number of colors.
Vehicle routine problem
To find the minimum cost vehicle routine so that
(i) every customer is visited exactly once by every
vehicle.
Graph coloring problem
Coloring a graph with minimum number of colors.
Vehicle routine problem
To find the minimum cost vehicle routine so that
(i) every customer is visited exactly once by every
vehicle.
(ii) the total demand does not exceed the vehicle
capacity.
Graph coloring problem
Coloring a graph with minimum number of colors.
Vehicle routine problem
To find the minimum cost vehicle routine so that
(i) every customer is visited exactly once by every
vehicle.
(ii) the total demand does not exceed the vehicle
capacity.
(iii) total length of tour does not exceed a certain
bound
Graph coloring problem
Coloring a graph with minimum number of colors.
Vehicle routine problem
To find the minimum cost vehicle routine so that
(i) every customer is visited exactly once by every
vehicle.
(ii) the total demand does not exceed the vehicle
capacity.
(iii) total length of tour does not exceed a certain
bound
(iv) Every vehicle comes back to the depot.
(e) Conclusion
(e) Conclusion
As in the case of neural networks, genetic
algorithms, and interior point algorithms,
this algorithm may not take you to the
optimum.
(e) Conclusion
As in the case of neural networks, genetic
algorithms, and interior point algorithms,
this algorithm may not take you to the
optimum.
Instead it takes you to a very good solution
with a very low cost (no.of iter.,
computational time etc)
Sequential ordering
problem