Table 6 Details of benchmark test functions.

From: Optimizing interval type-2 fuzzy logic PID controller with an improved constraint differential evolution algorithm

Instance

\(\:\varvec{n}\)

\(\:\varvec{L}\varvec{I}\)

\(\:\varvec{N}\varvec{I}\)

\(\:\varvec{L}\varvec{E}\)

\(\:\varvec{N}\varvec{E}\)

\(\:\varvec{\rho\:}\)

\(\:\varvec{f}\)

G01

13

9

0

0

0

0.011%

-15

G02

20

0

2

0

0

99.997%

-0.804

G03

10

0

0

0

1

0

-1.001

G04

5

0

6

0

0

51.123%

-30665.539

G05

4

2

0

0

3

0

5126.497

G06

2

0

2

0

0

0.007%

-6961.814

G07

10

3

5

0

0

0.001%

24.306

G08

2

0

2

0

0

0.856%

-0.096

G09

7

0

4

0

0

0.512%

680.630

G10

8

3

3

0

0

0.001%

7049.248

G11

2

0

0

0

1

0

0.749

G12

3

0

1

0

0

4.771%

-1

G13

5

0

0

0

3

0

0.054

G14

10

0

0

3

0

0

-47.765

G15

3

0

0

1

1

0

961.715

G16

5

4

34

0

0

0.020%

-1.905