4.3 Results
The detailed results (mean and standard deviation) are presented
in Tables 1-3 in Appendix. To illustrate the significance of the
results, the p-value for Mann-Whitney U test (rank-sum test)
comparing the averaged best function error values of MultiEA
with each of the other algorithms are listed. In the tables, a pvalue less than 0.05 (α=0.05) corresponds to significance in the
comparison result. Values shown in bold means that the
associated algorithm is significantly outperformed by MultiEA;
while underlined values mean that MultiEA is significantly
outperformed by the other algorithm. If the mean and/or the
standard deviation returns “0.00E+00”, it simply means that the
value is smaller than the smallest precision of floating point
number of Matlab.
MultiEA significantly outperforms AMALGAM-SO, PAP and
RandEA in 13, 18 and 21 out of 25 test functions; while it is
significantly outperformed by AMALGAM-SO, PAP and
RandEA in 9, 3 and 4 test cases, respectively. Since MultiEA
performs better than AMALGAM-SO and PAP, two state of the
art multiple algorithm approaches, this confirms the power and
potential of MultiEA. Moreover, MultiEA outperforms RandEA.
This suggests that by putting the algorithms in a portfolio using
our method, a positive synergy of the algorithms is achieved.