Table 8 Data for six indicators (D = 20).

From: HEPSO-SMC: a sliding mode controller optimized by hybrid enhanced particle swarm algorithm for manipulators

Function

Name

NFE

OT

SO

OA

CS

C

CR

F1

HEPSO

1

0.8

1

1

3.8

0.2

0.2

PSO

0.2

1

0.8

0.8

2.8

1

1

PSO-ST

1

0.4

0.4

0.4

2.2

0.2

0.2

UPS

1

0.6

0.2

0.2

2

0.2

0.2

WOA

1

0.2

0.6

0.6

2.4

0.2

0.2

F2

HEPSO

0.6

0.8

0.8

0.8

3

1

0.6

PSO

0.2

1

1

1

3.2

0.6

0.8

PSO-ST

0.8

0.4

0.4

0.6

2.2

0.4

0.4

UPS

1

0.6

0.2

0.2

2

0.2

0.2

WOA

0.4

0.2

0.6

0.4

1.6

0.8

1

F3

HEPSO

0.6

0.8

1

1

3.4

1

0.4

PSO

1

1

0.8

0.2

3

0.4

1

PSO-ST

0.2

0.4

0.6

0.4

1.6

0.8

0.2

UPS

0.4

0.6

0.2

0.8

2

0.6

0.6

WOA

0.8

0.2

0.4

0.6

2

0.2

0.8

F4

HEPSO

0.6

0.8

1

1

3.4

1

0.4

PSO

1

1

0.8

0.6

3.4

0.4

1

PSO-ST

0.2

0.4

0.6

0.8

2

0.8

0.2

UPS

0.4

0.6

0.2

0.4

1.6

0.6

0.6

WOA

0.8

0.2

0.4

0.2

1.6

0.2

0.8

F5

HEPSO

0.8

0.8

1

0.6

3.2

1

0.6

PSO

1

1

0.8

0.4

3.2

0.4

1

PSO-ST

0.2

0.4

0.6

1

2.2

0.8

0.2

UPS

0.4

0.6

0.4

0.8

2.2

0.2

0.4

WOA

0.6

0.2

0.2

0.2

1.2

0.6

0.8

F6

HEPSO

0.8

0.8

1

1

3.6

0.6

0.8

PSO

0.6

1

0.8

0.8

3.2

1

0.6

PSO-ST

0.2

0.4

0.2

0.2

1

0.4

0.2

UPS

0.4

0.6

0.4

0.4

1.8

0.2

0.4

WOA

1

0.2

0.6

0.6

2.4

0.8

1

F7

HEPSO

0.8

0.8

1

1

3.6

0.4

0.8

PSO

1

1

0.4

0.2

2.6

1

0.6

PSO-ST

0.2

0.4

0.8

0.6

2

0.6

0.2

UPS

0.6

0.6

0.2

0.4

1.8

0.2

0.4

WOA

0.4

0.2

0.6

0.8

2

0.8

1

F8

HEPSO

1

0.8

0.8

0.6

3.2

0.2

0.2

PSO

0.2

1

0.4

0.2

1.8

1

1

PSO-ST

0.4

0.4

0.6

0.8

2.2

0.6

0.6

UPS

0.6

0.6

0.2

1

2.4

0.8

0.8

WOA

0.8

0.2

1

0.4

2.4

0.4

0.4

F9

HEPSO

0.8

0.8

0.6

0.6

2.8

0.2

0.6

PSO

0.4

1

0.4

0.4

2.2

1

0.8

PSO-ST

0.2

0.4

1

1

2.6

0.8

0.2

UPS

0.6

0.6

0.2

0.2

1.6

0.6

0.4

WOA

1

0.2

0.8

0.8

2.8

0.4

1

F10

HEPSO

0.6

0.8

1

1

3.4

0.8

0.6

PSO

1

1

0.8

0.2

3

1

1

PSO-ST

0.2

0.4

0.8

0.8

2.2

0.6

0.2

UPS

0.4

0.6

0.2

0.4

1.6

0.2

0.4

WOA

0.8

0.2

0.6

0.6

2.2

0.4

0.8

F11

HEPSO

1

0.8

1

1

3.8

1

0.8

PSO

0.6

1

0.8

0.2

2.6

0.2

0.4

PSO-ST

0.2

0.4

0.4

0.8

1.8

0.6

0.2

UPS

0.4

0.6

0.2

0.4

1.6

0.4

0.6

WOA

0.8

0.2

0.6

0.6

2.2

0.8

1

F12

HEPSO

0.4

0.8

0.8

0.8

2.8

0.6

0.6

PSO

1

1

0.6

0.2

2.8

1

1

PSO-ST

0.2

0.4

0.4

0.6

1.6

0.2

0.2

UPS

0.6

0.6

0.2

0.4

1.8

0.4

0.4

WOA

0.8

0.2

1

1

3

0.8

0.8

  1. Significant values are in bold, the larger the value of CS, the better.