Figure 3. Example of a satellite image obtained with the QuickBird Sensor RGB – 432
4.1 Highest Fitness Value
Obtaining the higher possible fitness value also referred to as global minimum is the primary objective of stochastic methods
such as genetic programming. Therefore, highest fitness is the one major assessment criterion. Due to the randomness
associated with the development of the first generation in the genetic programming algorithm, the highest fitness generated in
each generation has no obvious regularity. Hence, multiple replications for each configuration were used. All diagrams in
Figure 4 illustrate the mean, minimum, maximum and standard deviation of all highest fitness obtained from each generation
when using different parameter setting. Investigations of population size demonstrate the relationship
between population size and mean, minimum, and standard deviation of all highest fitness is exponential and when the
population size is increased into 1,500, the growing trend of mean, minimum, and standard deviation become less noisy e.g.
Figure 4.X.1, Figure 4.X.2, and Figure 4.X.4. Although the exponential relationship between the population size and
highest fitness is not explicit, it can be noted that the growing trend of highest fitness become slowly when the population size
increasing into 1,500 e.g. Figure 4.1.3, Figure 4.2.3, and Figure 4.3.3 and Figure 4.4.3. These evidences demonstrate that the
difference of the performance is extremely small when the population size exceeds 1,500. However, the larger population
size will consume more computer resource e.g. CPU and Memory and execution time. There is a tradeoff between
computational time and additional generations additional iterations. Therefore, the optimal population size derived from
results of the fitness exploration stage is around 1,500. Regarding the percentage of mutation and crossover, the results
reflect that there is no significant difference between the mean, minimum, maximum and standard deviation of top fitness
values when using different parameter setting. However, it still worth noting that better performance arises from higher
percentage of mutation and crossover and the growing trend of mean, maximum, minimum, and standard deviation of all
highest fitness becomes smother when increasing the total percentage of mutation and crossover. This can be attributed to
higher percentages of crossover and mutation contributes to increased population diversity and therefore faster convergence.
When the total percentage is 20, the best percentage of mutation is arranges from 12 to 20 that is, the percentage
of crossover is result of using 20 subtract the percentage of mutation and the remaining 80 is replication. When the total
percentage is 30 or 40, mutation is arrange 25 to 30 and from 30 to 40, respectively. Moreover, the performance of
mutation over crossover and crossover over mutation indicate the optimal order of mutation and crossover is mutation over
crossover when the total percentage of mutation and crossover is 20.
Figure 4.1.1 Mean Fitness of All Highest Fitness
Figure 4.1.2 Minimum Fitness of All Highest Fitness
Figure 4.1.3 Maximum Fitness of All Highest Fitness
Figure 4.1.4 Standard Deviation of All Highest Fitness
Figure 4.1 Total Percentage of Mutation and Crossover is 20 Crossover over Mutation
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
100 400
700 1000
1300 1600
1900 0.65
0.66 0.67
0.68 0.69
0.7 0.71
0.72 0.73
0.74 0.75
0.76 0.77
0.78 0.79
0.8 0.81
0.82 0.83
0.84 0.85
0.86 0.87
0.88 0.89
0.9 0.91
0.92 0.93
0.94 0.95
Percentage of Mutation Population Size
M e
a n
o f
A ll
H ig
h e
s t
F it
n e
s s
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
100 400
700 1000
1300 1600
1900 0.12
0.15 0.18
0.21 0.24
0.27 0.3
0.33 0.36
0.39 0.42
0.45 0.48
0.51 0.54
0.57 0.6
0.63 0.66
0.69 0.72
0.75 0.78
0.81 0.84
0.87 0.9
0.93
Percentage of Mutation Population Size
M in
im u
m o
f A
ll H
ig h
e s
t F
it n
e s
s
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
100 400
700 1000
1300 1600
1900 0.935
0.936 0.937
0.938 0.939
0.94 0.941
0.942 0.943
0.944 0.945
0.946 0.947
0.948 0.949
0.95 0.951
0.952 0.953
0.954 0.955
0.956 0.957
0.958 0.959
0.96
Percentage of Mutation Population Size
M a
x im
u m
o f
A ll
H ig
h e
s t
F it
n e
s s
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
100 400
700 1000
1300 1600
1900 0.01
0.02 0.03
0.04 0.05
0.06 0.07
0.08 0.09
0.1 0.11
0.12 0.13
0.14 0.15
0.16 0.17
0.18 0.19
0.2 0.21
0.22 0.23
0.24
Population Size Percentage of Mutation
S ta
n d
a rd
D e
v ia
ti o
n o
f A
ll H
ig h
e s
t F
it n
e s
s
ISPRS Technical Commission I Symposium, 17 – 20 November 2014, Denver, Colorado, USA
This contribution has been peer-reviewed. doi:10.5194isprsarchives-XL-1-113-2014
116
Figure 4.2.1 Mean Fitness of All Highest Fitness
Figure 4.2.2 Minimum Fitness of All Highest Fitness
Figure 4.2.3 Maximum Fitness of All Highest Fitness
Figure 4.2.4 Standard Deviation of All Highest Fitness
Figure 4.2 Total Percentage of Mutation and Crossover is 20 Mutation over Crossover
Figure 4.3.1 Mean Fitness of All Highest Fitness
Figure 4.3.2 Minimum Fitness of All Highest Fitness
Figure 4.3.3 Maximum Fitness of All Highest Fitness
Figure 4.3.4 Standard Deviation of All Highest Fitness
Figure 4.3 Total Percentage of Mutation and Crossover is 30 Mutation over Crossover
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
100 400
700 1000
1300 1600
1900 0.75
0.76 0.77
0.78 0.79
0.8 0.81
0.82 0.83
0.84 0.85
0.86 0.87
0.88 0.89
0.9 0.91
0.92 0.93
0.94
Percentage of Mutation Population Size
M e
a n
o f
A ll
H ig
h e
s t
F it
n e
s s
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
100 400
700 1000
1300 1600
1900 0.2
0.23 0.26
0.29 0.32
0.35 0.38
0.41 0.44
0.47 0.5
0.53 0.56
0.59 0.62
0.65 0.68
0.71 0.74
0.77 0.8
0.83 0.86
0.89 0.92
0.95
Percentage of Mutation Population Size
M in
im u
m o
f A
ll H
ig h
e s
t F
it n
e s
s
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
100 400
700 1000
1300 1600
1900 0.935
0.936 0.937
0.938 0.939
0.94 0.941
0.942 0.943
0.944 0.945
0.946 0.947
0.948 0.949
0.95 0.951
0.952 0.953
0.954 0.955
0.956 0.957
0.958 0.959
0.96
Percentage of Mutation Population Size
M a
x im
u m
o f
A ll
H ig
h e
s t
F it
n e
s s
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
100 400
700 1000
1300 1600
1900 0.005
0.01 0.015
0.02 0.025
0.03 0.035
0.04 0.045
0.05 0.055
0.06 0.065
0.07 0.075
0.08 0.085
0.09 0.095
0.1 0.105
0.11 0.115
0.12 0.125
0.13 0.135
0.14 0.145
0.15 0.155
0.16
Population Size Percentage of Mutation
S ta
n d
a rd
D e
v ia
ti o
n o
f A
ll H
ig h
e s
t F
it n
e s
s 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
100 400
700 1000
1300 1600
1900 0.8
0.81 0.82
0.83 0.84
0.85 0.86
0.87 0.88
0.89 0.9
0.91 0.92
0.93 0.94
0.95 0.96
Percentage of Mutation Population Size
M e
a n
o f
A ll
H ig
h e
s t
F it
n e
s s
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 100
400 700
1000 1300
1600 1900
0.32 0.34
0.36 0.38
0.4 0.42
0.44 0.46
0.48 0.5
0.52 0.54
0.56 0.58
0.6 0.62
0.64 0.66
0.68 0.7
0.72 0.74
0.76 0.78
0.8 0.82
0.84 0.86
0.88 0.9
0.92 0.94
Percentage of Mutation Population Size
M in
im u
m o
f A
ll H
ig h
e s
t F
it n
e s
s
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 100
400 700
1000 1300
1600 1900
0.941 0.942
0.943 0.944
0.945 0.946
0.947 0.948
0.949 0.95
0.951 0.952
0.953 0.954
0.955 0.956
0.957 0.958
0.959 0.96
Percentage of Mutation Population Size
M a
x im
u m
o f
A ll
H ig
h e
s t
F it
n e
s s
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
21 22
23 24
25 26
27 28
29 30
100 400
700 1000
1300 1600
1900 0.005
0.01 0.015
0.02 0.025
0.03 0.035
0.04 0.045
0.05 0.055
0.06 0.065
0.07 0.075
0.08 0.085
0.09 0.095
0.1 0.105
0.11 0.115
0.12
Population Size Percentage of Mutation
S ta
n d
a rd
D e
v ia
ti o
n o
f A
ll H
ig h
e s
t F
it n
e s
s
ISPRS Technical Commission I Symposium, 17 – 20 November 2014, Denver, Colorado, USA
This contribution has been peer-reviewed. doi:10.5194isprsarchives-XL-1-113-2014
117
Figure 4.4.1 Mean Fitness of All Highest Fitness
Figure 4.4.2 Minimum Fitness of All Highest Fitness
Figure 4.4.3 Maximum Fitness of All Highest Fitness
Figure 4.4.4 Standard Deviation of All Highest Fitness
Figure 4.4 Total Percentage of Mutation and Crossover is 40 Mutation over Crossover
Figure 4. Mean, Min, Max and Standard Deviation of all highest fitness generated in each generation for various population size and percentage
of mutation and crossover
4.2 Computation Time:
Kategori