Table 5 Wilcoxon signed-rank test outcomes for 26 well-known benchmark functions at a significance level of \(\alpha = 0.05.\).

From: Cooperative metaheuristic algorithm for global optimization and engineering problems inspired by heterosis theory

Algorthm

Better

Equal

Worse

P-value

Symbol

Effect size

CMA-PSO

25

1

0

1.229E-05

\(+\)

0.85749

CMA-ACO

26

0

0

1.0503E-05

\(+\)

0.8642

CMA-BES

21

3

2

7.3532E-04

\(+\)

0.6621

CMA-DE

26

0

0

8.2981e-06

\(+\)

0.87416

CMA-BOA

21

1

4

3.6367E-03

\(+\)

0.57032

CMA-GWO

20

0

6

4.8186E-02

\(+\)

0.31939

CMA-WOA

20

1

5

3.4482E-02

\(+\)

0.41465

CMA - PS-BES

20

4

2

5.4503E-04

\(+\)

0.69152

CMA-PSOBOA

20

2

4

2.0675E-04

\(+\)

0.72771

CMA-HPSOBOA

17

2

9

5.1103E-03

\(+\)

0.56