Table 3 Summary of results obtained for different benchmark functions (Case 1).

PSO³¹

mean

0.066667

9.89E − 08

4.12E − 02

7.79E − 05

1078.0941

std

0.253721

4.88E − 07

1.72E − 02

1.39E − 04

647.25346

WOA³¹

mean

0

2.48E − 208

3.67E − 04

3.90E − 117

977.52989

std

0

0

3.61E − 04

1.11E − 116

866.21494

SSA³¹

mean

5.13333

5.22E − 09

1.31E − 02

0.16395

5.49E − 04

std

2.93297

8.73E − 10

5.21E − 03

0.33186

8.73E − 04

TLBO³¹

mean

0

7.06E − 87

1.02E − 03

9.40E − 44

2.16E − 16

std

0

1.02E − 86

2.96E − 04

6.87E − 44

6.13E − 16

AHA³¹

mean

0

7.32E − 292

6.06E − 05

8.99E − 150

2.96E − 278

std

0

0

4.83E − 05

3.87E − 155

0

COLAHA

(Proposed)

mean

0

0

1.95E-07

4.10E-177

3.8068e-316

std

0

0

1.11E-07

0

0

PSO³¹

mean

49.164576

0

0

30.845624

0

std

30.081342

0

0

7.6342136

0

WOA³¹

mean

25.15995

0

4.19E − 07

0

0

std

0.2677

0

3.25E − 07

0

0

SSA³¹

mean

48.64191

3.52E − 12

2.52E − 15

33.79541

1.41E − 16

std

48.27414

4.70E − 12

3.27E − 15

14.36489

2.57E − 16

TLBO³¹

mean

23.377421

0

0

12.679728

0

std

0.703925

0

0

5.5850898

0

AHA³¹

mean

25.065057

0

0

0

0

std

0.278139

0

0

0

0

COLAHA

(Proposed)

mean

14.9501

0

0

0

0

std

0.0868

0

0

0

0

PSO³¹

mean

0.605883

1.19E − 03

9.97E − 02

0.177466

7.69E − 03

std

0.739731

2.91E − 03

0.380955

0.280077

1.45E − 02

WOA³¹

mean

0.8788

4.36E − 01

2.90E − 15

4.35E − 06

1.94E − 03

std

1.23697

4.07E − 01

2.22E − 15

1.61E − 06

8.19E − 03

SSA³¹

mean

3.57E − 03

1.33E − 02

1.2144

1.37761

2.93E − 03

std

2.96E − 03

2.48E − 02

0.97792

1.37411

4.94E − 03

TLBO³¹

mean

2.18E − 02

1.88E − 03

6.57E − 15

3.46E − 03

4.26E − 02

std

4.04E − 02

2.36E − 03

1.77E − 15

1.89E − 02

4.90E − 02

AHA³¹

mean

4.94E − 02

1.45E − 04

8.88E − 16

4.15E − 07

0.669596

std

0.120376

1.79E − 04

0

5.63E − 07

0.547843

COLAHA

(Proposed)

mean

0.0357

8.80E-06

8.88E-16

1.98E-09

0.0756

std

0.072

2.42E-05

0

2.24E-09

0.106