Table 2 The details of benchmark functions.

From: An Adaptive Cultural Algorithm with Improved Quantum-behaved Particle Swarm Optimization for Sonar Image Detection

Function

Name

Searching range

Global optimum

Dimension

Modality

F1

Sphere

[−5.12, 5.12]

0

10/30/50

unimodal

F2

Generalized Griewank

[−600, 600]

0

10/30/50

multimodal

F3

Stretched_V sine

[−10, 10]

0

10/30/50

multimodal

F4

Generalized Rastrigin’s

[−5.12, 5.12]

0

10/30/50

multimodal

F5

Generalized Rosenbrock’s

[−2.048, 2.048]

0

10/30/50

unimodal

F6

Quartic

[−1.28, 1.28]

0

10/30/50

unimodal

F7

Schwefel’s problem 2.22

[−10, 10]

0

10/30/50

unimodal

F8

Alpine

[−10, 10]

0

10/30/50

multimodal

F9

Salomon

[−100, 100]

0

10/30/50

multimodal

F10

Zakharov

[−5, 10]

0

10/30/50

unimodal