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final claims; first, we apply the Kolmogorov-Smirnov test on the data to check
their normality; if they are normally distributed the ANOVA test is performed,
otherwise we will apply a Kruskal-Wallis test. The confidence level used for our
claims is 95%.
We always consider in this work a confidence level of 95% (i.e., significance
level of 5% or
p
-value under 0.05) in the statistical tests, which means that the
differences are unlikely to have occurred by chance with a probability of 95%.
Successful tests are marked with + symbol,
•
means that no statistical confidence
was found (
p
-value
<
0
.
05).
The experiments was performed using the host with a CPU Intel(R) i7 CPU
920, with a total physical memory of 8192 MB. The operating system is Ubuntu
Precise 12.04. In the case of the GPU, we have an NVIDIA GeForce GTX 680
with 2048 MB of DRAM on device and we used CUDA version 6.0.
5 Analysis and Results
In this section, we show the experimental results obtained by testing our pro-
posed method and the behaviour of GPU-FAP is discussed. First, we present a
detailed analysis about numerical and time performance for both DNA-FAP and
TSP instances. Finally, we study the scalability of our approach and compare
the gain times with respect to CPU-DFA version.
DNA-FAP Results.
Table 2 shows the results for all the DNA-FAP instances
with the different configurations for
p
and
m
. In the first column, we inform the
name chosen for the instance, columns two and three show the diverse values
assumed by parameters
p
and
m
. For CPU-DFA, columns four, five and six
indicate in 30 independent runs the best fitness (Best) found, the average fitness
value with its standard deviation and average runtime, respectively. In the case
of GPU-DFA, the same data are exposed in columns seven, eight and nine.
Among the results for both implementations, they generate fitness values that
are closer to the overall one, while even in some instances, they reach it. Table
2 shows that the two versions found the optimal value at least once for instance
x
60189
4
in all the configurations. For the rest of instances, both versions (CPU
and GPU) obtain values located really quite near to the optimal one. In par-
ticular for the second DNA-FAP instance (
m
154216
6
), both versions found the
best known optimal value with one configuration. For the instance
bx
842596
4
the
increase in parameters
p
and
m
does not mean an improvement in the quality
of the results; moreover, their quality worsens.
Regarding the results related to parameter
p
, for instance
x
60189
4
shows that
there are no differences; all variations reach the optimum value. For the other two
instances, the fitness values obtained are very close to the best optimum one with
p
=32for
m
154216
6
and
p
=16for
bx
842596
4
. With respect to parameter
m
,
the best configuration is obtained with
m
= 32, exhibiting the same behaviour
in most of the instances that are very close to the optimal one. We can also note
that for parameter
m
= 48 we obtained shorter times for all the instances.
