5.2 Results
The detailed results (mean, standard deviation and p-value using
U test) are presented in Tables 1-3 in Appendix. Fig. 1 presents a
summary of the statistical hypothesis test results.
Fig. 1 Summary of the result comparison between MultiEA and
five other prediction measures. “+” means MultiEA significantly
outperforms another algorithm; “-” means the opposite.
It can be observed that MultiEA outperforms the other algorithms
in a neck to neck comparison.
Comparing with MultiEA1 and MultiEA2, the result suggests that
the use of a probability distribution is a good strategy for
modeling the evolution tendency of component algorithms than a
single mean/median point. MultiEA3 may put too much strength
on the latest data points. MultiEA4 put equal weight on all data
points since it randomly chooses two points and doing a
prediction. MultiEA outperforms both MultiEA3 and MultiEA4,
which means that MultiEA attains a better balance in the use of
data points than these two algorithms. MultiEA5 utilizes a
histogram to select algorithm. The histogram roughly estimates
the distribution of the predicted values. This is why MultiEA5
only obtains slightly worse results than MultiEA.
Through the study of five different prediction measures, we can
conclude that the proposed method could organize well the
predicted values by forming a bootstrap distribution and identify
the evolution tendency of component algorithms. Therefore,
MultiEA achieves good performance (on experimental results on
CEC 2005 test suite).
Note that MultiEA5 is only marginally worse than MultiEA. Thus
it is an attractive alternative.