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Table 1.
Parameters of Moving Peaks Benchmark
Parameter
Value
number of peaks
10
f
every 5000 evaluations
height severity
7.0
width severity
1.0
peak shape
cone
shift length s
{0.0}
number of dimensions D
5
A
[0, 100]
H
[30.0, 70,0]
W
[1, 12]
I
50.0
The default parameter setting of MPB used in the experiments is presented in
Table 1. In MPB, shift length,
s
, is the radius of peak movement after an environment
change.
m
is the number of peaks.
f
is the frequency of environment change as
number of fitness evaluations.
H
and
W
denote range of height and width of peaks
which will change after a change in environment by height severity and width severity
respectively.
I
is the initial heights for all peaks. Parameter
A
denotes minimum and
maximum value on all dimensions. For evaluating the efficiency of the algorithms, we
use the offline error measure, the average deviation of the best individual from the
optimum in all iterations
.
Table 2.
Offline error ±Standard Error for f =500 and f =1000
Proposed
algorithm
f=500
MultiSw
armPSO
f=500
CellularP
SO f=500
FMSO
f=500
mQSO10
f=500
Proposed
algorith
m f=1000
MultiSw
armPSO
f=1000
CellularP
SO
f=1000
FMSO
f=1000
mQSO10
f=1000
1
12.49±0.21
5.46
±0.30
13.4±0.74
27.58±0.9
33.67±3.4
6.12±0.22
2.90
±0.18
6.77±0.38
14.42±0.4
18.6±1.6
5
11.87±0.24
5.48
±0.19
9.63±0.49
19.45±0.4
11.91±0.7
5.66±0.20
3.35
±0.18
5.30±0.32
10.59±0.2
6.56±0.38
10
9.26±0.12
5.95
±0.09
9.42±0.21
18.26±0.3
9.62±0.34
5.88±0.16
3.94
±0.08
5.15±0.13
10.40±0.1
5.71±0.22
7.39±0.17
6.45
±0.16
8.84±0.28
17.34±0.3
9.07±0.25
5.36±0.16
4.33
±0.12
5.23±0.18
10.33±0.1
5.85±0.15
20
30
7.74±0.11
6.60
±0.14
8.81±0.24
16.39±0.4
8.80±0.21
5.37±0.16
4.41
±0.11
5.33±0.16
10.06±0.1
5.81±0.15
40
6.32
±0.14
6.85±0.13
8.94±0.24
15.34±0.4
8.55±0.21
4.45
±0.11
4.52±0.09
5.61±0.16
9.85±0.11
5.70±0.14
50
5.97
±0.16
7.04±0.10
8.62±0.23
15.54±0.2
8.72±0.20
4.49
±0.15
4.57±0.08
5.55±0.14
9.54±0.11
5.87±0.13
100
5.65
±0.12
7.39±0.13
8.54±0.21
12.87±0.6
8.54±0.16
3.79
±0.09
4.77±0.08
5.57±0.12
8.77±0.09
5.83±0.13
5.55
±0.11
7.52±0.12
8.28±0.18
11.52±0.6
8.19±0.17
3.93
±0.10
4.76±0.07
5.50±0.12
8.06±0.07
5.54±0.11
200
In the proposed method the acceleration coefficients
c
1
and
c
2
are set to 2.8 and 1.3
and the inertial weight
w
is set to mean of
c
1
and
c
2
(2.05). The number of particles in
the swarm is set to 20 particles. Parameters
d
11
,
d
21
,
d
12
,
d
22
,
v
1
and
v
2
are user-
specified which are experimentally set to 0.4, 0.4, 0.6, 0.6, 0.4 and 0.6 respectively.
The proposed algorithm is compared with Multi-Swarm PSO [9], mQSO [1], FMSO
[16], and cellular PSO [6]. In Multi-Swarm PSO the acceleration coefficients
c
1
and
c
2
are set to 1.496180 and the inertial weight
w
is set to 0.729844. The number of
particles in the parent swarm and the child swarms (π) are set to 5 and 10 particles,
respectively in Multi-Swarm PSO. The radius of the child swarms (
r
), the minimum
allowed distance between two child swarm (
rexcl
) and the radius of quantum particles
(
rs
) are set to 30.0, 30.0, and 0.5, respectively. For mQSO we adapted a configuration
10(5+5q) which creates 10 swarms with 5 neutral (standard) particles and 5 quantum
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