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Table 1 Performance evaluation of ISCA over SCA, SSA, ALO, and PSO with the results of unimodal and multimodal benchmark test function

From: Design of a 2-DOF-PID controller using an improved sine–cosine algorithm for load frequency control of a three-area system with nonlinearities

Function

ISCA

SCA

ALO

SSA

PSO

Mean

SD

Mean

SD

Mean

SD

Mean

SD

Mean

SD

F1

9.861E−23

1.9902E−22

5.09E−07

1.8181E−06

2.78E−08

5.51E−08

6.73E−05

2.78E−05

4.71E−19

1.95E−18

F2

1.6083E−13

2.55799E−13

5.92E−07

1.05E−06

8.52E−01

1.438721

1.67E−01

0.471005

1.4E−10

2.21E−10

F3

1.8392E−11

4.72532E−11

1.184673

2.160575127

4.31E−01

0.94951

4.81E−01

1.023026

0.002479

0.002992

F4

1.2235E−07

1.9916E−07

0.645629

2.739876

5.12E−03

0.006441

7.12E−03

0.00271

0.002384

0.003236

F5

7.28815

0.74182571

7.82433

0.488597

7.439

0.48539

7.8815

0.74182571

7.715811

10.01262

F6

1.02E−01

0.144505681

6.17E−01

0.239647

1.13E−08

6.74E−09

8.50E−05

2.96E−05

9.82E−20

2.35E−19

F7

0.00166489

0.001521864

0.004657

0.004711

5.42E−02

0.05512

5.24E−02

0.011685

0.003652

0.001909

F8

−2592.82

235.4926943

−2034.37

163.8136

− 2.32E+03

482.0453

− 2.72E+03

331.762

− 3547.06

234.6265

F9

2.180495

3.160774643

1.706543

4.872987

1.90E+01

9.676224

2.52E+01

8.30621

13.008369

6.522

F10

2.9915E−13

7.306E−13

1.4693E−6

4.5680E−6

5.00E−04

0.8121E−4

1.08E−2

0.7864E−01

6.78E−09

1.17E−9

F11

0.0436073

0.052779053

0.174077

0.173886

0.2324

0.27878

0.6492

0.714695

0.2326

0.27978

F12

0.02507793

0.01997888

0.148819

0.056735

2.73E+00

3.125277

7.05E−01

1.118442

1.11E−19

2.92E−19

F13

0.08798077

0.076773756

0.031108

0.099245

2.15E−03

0.00558

5.97E−03

0.00815

0.1137

0.1957

  1. Bold value shows the best value