rank 1 5 4 7 6 2 3

Case 9 success% 100 2 0 2 52 98 100

mean_time 108。38 999。29 1000 999。48 748。79 206。56 237。65

std_time 27。48 5。08 0 3。74 314。80 189。82 234。70

p time – 4。73E—20⁄ 3。30E—20⁄ 4。73E—20⁄ 7。21E—18⁄ 7。61E—10⁄ 8。81E—10⁄

rank 1 5 7 6 4 3 2

Average rank 1 5。11 6 6 4。88 2。44 2。55

a   success%: The value denotes the success rate among 50 runs。

b   mean_time: The value is the mean of search time among 50   runs。

c   std_time: The value is the standard error of search time among 50 runs。

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

e   rank: Composite ranking is applied to all of algorithms, which is evaluated by the descending order of success rate and the ascending order of searchtime。f

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

Table 12

Statistical results obtained by the Wilcoxon signed ranks test for pairwise comparisons based on nine scenarios for three and five robots。

Comparison Rþa R— b p value Comparison Rþ R—