![](bg6.png)
duced by Shekel’s function.
0
0.2
0.4
0.6
0.8
1
50 100 150 200 250 300 350 400 450 500
Fitness
Generations
Shekle’s Foxholes Performance Analysis - SGA & MMGA
Off-line Performance SGA
On-line Performance SGA
Off-line Performance MMGA
On-line Performance MMGA
Figure 10: Shekel’s Foxholes - SGA & MMGA.
5.6 Statistical Results
A Wilcoxon rank sum test was used to test for statis-
tically significant between the SGA and MMGA and
the results are outlined in Table 4.
Table 4: Wilcoxon Ranksum Test Results.
Function Results Statistical Significance
f
1
Off-Line Highly Significant
f
1
On-Line Highly Significant
f
2
Off-Line Highly Significant
f
2
On-Line Highly Significant
f
3
Off-Line Highly Significant
f
3
On-Line Highly Significant
f
4
Off-Line Highly Significant
f
4
On-Line Not Significant
f
5
Off-Line Highly Significant
f
5
On-Line Highly Significant
6 CONCLUSIONS
Overall the experiments conducted show that for
the characteristics present in the Sphere function,
the Rosenbrock function, the Step function and the
Quadratic function, the benefit of neutrality is not ap-
parent at first sight and for many it is negligible. How-
ever, this is not the case for the Sheckel’s Foxholes
experiments, where the introduction of neutrality into
the GP-map has been shown to be beneficial. By in-
cluding an adaptation of the biological concepts of
transcription and translation into a GA to introduce
neutrality into the GP-map, the results of the exper-
iments over the modified De Jong test suite, indicate
classes of problemswhich could possibly benefit from
the inclusion of a multi-layered GP-map. The results
appear to suggest that the problems most likely to
benefit would contain a combination of characteris-
tics such as, low-dimensionality,multi-modality, non-
separable, continuous and deterministic.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the support of
NUI Galway’s Millennium Fund.
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