Information Technology Reference
In-Depth Information
4
Evaluation
In this section we evaluate our features and build a classifier which computes specific
parameter sets for the Particle Swarm Optimization on a specific function. This opti-
mization should have a better performance compared to the PSO on the same function
with standard parameter set.
Ta b l e 1 .
Overview of the function pool and the initialization areas
Function
Optimum
Domain
Initialization
[
−
32
,
32]
n
[16
,
32]
n
Ackley
x
i
=0
Gen. Schwefel
x
i
= 420
.
9687 [
−
500
,
500]
n
[
−
500
, −
250]
n
[
−
600
,
600]
n
[300
,
600]
n
Griewank
x
i
=0
[
−
5
.
12
,
5
.
12]
n
[2
.
56
,
5
.
12]
n
Rastrigin
x
i
=0
[
−
30
,
30]
n
[15
,
30]
n
Rosenbrock
x
i
=1
[
−
100
,
100]
n
[50
,
100]
n
Schwefel
x
i
=0
[
−
100
,
100]
n
[50
,
100]
n
Sphere
x
i
=0
4.1
Experimental Setup
We choose 7 test functions out of the suggested test function pool from [3] and stop
computing the fitness function after 300000 times. With our swarm size of 30 the num-
ber of epochs is consequently set to 10000. We define a run as a parameter set which
is tested 90 times with a finite set of different seed values in order to get meaningful
results. As topology of the swarm
gbest
is used. The initialization of the particle is in
a defined square of the search space (see table 1). Before we start to train our classifier
with the features we have to create the classes that represent specific parameter sets
with a high quality of the optimization performance.
4.2
Finding the Best Parameter
In order to find the best parameter set for each function (see table 1), we start an
extensive search with respect to the continuous values. We try to focus on real val-
ues with a precision of four decimal places. The standard parameter set for PSO is
ω
=(
W, C
1
,C
2
)
with
W
=0
.
72984
and
C
1
=
C
2
=1
.
4962
. For the extensive exami-
nation of parameters we take into account the intervals
W
[0
,
2
.
5]
.
We create a sequence between this interval values based on the standard value with
a exponential factor of
(
∈
[0
,
1]
and
C
1
,C
2
∈
1+
√
5
)
x
where
x
indicates the sequence number. We calcu-
late 13 and 23 sequence values around the standard value and obtain a sequence of
values between the intervals. Depending on the exponential factor the values close
by the standard values have a lower distance to each other than the values closer to
the borders of the interval. In figure 5 our configuration space of the extensive search
is plotted. With all possible combinations of the single parameter values we examine
13
2
23 = 6877
different parameter sets and test each of them for every function
90 times. As described above, we analyze the data of the extensive search by comparing
the results of each configuration's optimization process on a function. We choose the
×
23
×
