p value – 4。95E—06⁄ 9。43E—14⁄ 1。17E—04⁄ 1。49E—06⁄ 3。01E—11⁄ 6。88E—05⁄ 3。33E—11⁄

f10 mean 5。33E+03 6。50E+03 7。99E+03 6。61E+03 4。11E+03 7。83E+03 6。64E+03 3。69E+03

best 4。07E+03 3。97E+03 3。42E+03 3。28E+03 2。06E+03 4。56E+03 4。38E+03 2。56E+03

std 8。91E+02 1。58E+03 2。40E+03 1。50E+03 9。75E+02 1。63E+03 1。33E+03 4。43E+02

p value – 1。80E—03⁄ 1。58E—08⁄ 6。14E—04⁄ 1。07E—05⁄ 3。86E—08⁄ 2。44E—05⁄ 1。05E—10⁄

Summary func bf – 9 10 8 6 8 6 7

func wg – 1 0 1 3 0 2 1

a   mean: The value denotes the mean function error based on 50 runs。

b   best: The value is the minimal function error among 50  runs。

c    std: The value denotes  the  standard error based  on 50  runs。

d p value: The value is a p value of a two-sample Wilcoxon rank sum test for the function error between the DFPSO algorithm and the other comparison algorithms in the corresponding column。 The p value being smaller means that the results obtained by the DFPSO algorithm are significant compared with the ones achieved by the other    algorithms。

e

m:  The  difference  between  two  samples  is  significant  at  a  level  a ¼ 0:05。

f   func b: The number of functions where the DFPSO algorithm obtains significantly better results。

g   func w: The number of functions where the DFPSO algorithm obtains significantly worse results。