Table 7 The Average and Std ranks of nine algorithms using Friedman’s test based upon their results on the 23 test functions.

From: Enhancing grasshopper optimization algorithm (GOA) with levy flight for engineering applications

Algorithm

Average

Std

Mean rank

Diff with LFGOA

Std Rank

Diff with LFGOA

AHA

3.782608696

1.3043 < 2.5051

3.217391304

0.9565 < 2.5051

AO

4.434782609

1.9565 < 2.5051

4.000000000

1.7391 < 2.5051

DA

6.478260870

4.0000 > 2.5051

6.695652174

4.4348 > 2.5051

DMOA

6.043478261

3.5652 > 2.5051

4.913043478

2.6522 > 2.5051

GBO

5.043478261

2.5652 > 2.5051

5.000000000

2.7391 > 2.5051

HGS

6.347826087

3.8696 > 2.5051

6.652173913

4.3913 > 2.5051

HHO

5.260869566

2.7826 > 2.5051

6.086956522

3.8261 > 2.5051

LFGOA

2.478260870

0

2.260869565

0

MVO

4.869565217

2.3913 < 2.5051

6.173913043

3.9130 > 2.5051