Table 4 Test result of unimodal benchmark functions with dim = 10.

HHO

3.8514E-210

3.7928E-191

1.7343E-200

0

0.001624583

HHO-Elite

0

3.853E-191

5.1661E-208

0

0.009184147

HHO-GA

1.05617E-11

2.30366E-07

8.36709E-08

3.49001E-07

0.0132108

HHO-CHAOS

1.6561E-203

6.4675E-187

1.1353E-195

0

0.002536153

HHO-ADAP

2.57644E-84

4.0665E-65

2.37138E-73

1.75929E-64

0.00337206

HHO-PSO

2.6538E-101

8.33657E-79

9.58239E-83

3.47562E-78

0.00114189

HHO-Inertia

6.31063E-84

6.46359E-67

1.56841E-70

2.10888E-66

0.000963807

HHO-ULTRA

9.28024E-15

0.000780372

3.09119E-05

0.001827781

0.01004731

WMA

17.27929546

77.17529671

54.65950052

55.879158

0.322219463

CMA-ES

1.16029E-42

8.0194E-41

4.10391E-41

1.55893E-40

0.125990187

EBOwithCMAR

1.21647E-34

8.31832E-30

9.30126E-31

1.69968E-29

0.18967836

L-SHADE

2.21414E-55

1.36039E-38

5.61703E-42

4.65157E-38

0.055415973

LSHADE-cnEpSin

6.84089E-47

3.68138E-34

2.13246E-34

4.50774E-34

0.770208807

SPS-L-SHADE-EIG

2.19369E-34

1.55792E-32

3.1448E-33

5.09035E-32

0.401865883

OWMA

6.64647E-18

1.4158E-16

1.15401E-16

1.38525E-16

0.31201546

F2

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

4.5532E-113

3.70132E-98

5.0926E-102

1.34699E-97

0.0030024

HHO-Elite

5.9964E-113

9.7515E-100

1.5211E-106

5.2448E-99

0.010697013

HHO-GA

5.6566E-07

2.95316E-05

2.36589E-05

2.42545E-05

0.004958337

HHO-CHAOS

1.9411E-102

2.96189E-94

3.35066E-97

1.01666E-93

0.00246326

HHO-ADAP

3.14527E-63

3.00153E-52

4.80265E-57

1.60195E-51

0.00150606

HHO-PSO

4.78146E-46

2.88796E-41

1.1464E-42

6.23406E-41

0.00181826

HHO-Inertia

6.53532E-39

2.16203E-35

3.4207E-36

5.53121E-35

0.000845663

HHO-ULTRA

1.27625E-09

0.002170083

0.000269195

0.004398259

0.00986834

WMA

2.891038132

15.36024532

14.6831427

6.531710866

0.31073477

CMA-ES

3.22125E-21

1.00151E-20

8.2534E-21

5.59568E-21

0.129767997

EBOwithCMAR

1.36703E-18

5.31208E-17

2.88487E-17

6.04242E-17

0.17156453

L-SHADE

2.18594E-28

3.52372E-21

9.79388E-23

6.6096E-21

0.052315513

LSHADE-cnEpSin

2.11091E-24

1.01544E-20

3.93426E-22

2.55474E-20

0.824555897

SPS-L-SHADE-EIG

5.87525E-18

2.56263E-17

2.13853E-17

1.67873E-17

0.355315563

OWMA

4.54527E-10

3.62768E-09

2.587E-09

4.84072E-09

0.28643924

F3

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

2.1347E-197

2.8449E-160

2.5448E-176

1.5582E-159

0.008059373

HHO-Elite

1.4506E-204

1.8632E-174

7.547E-182

0

0.016265793

HHO-GA

2.24057E-10

2.7909E-05

4.17618E-06

6.38826E-05

0.0118595

HHO-CHAOS

1.0946E-198

2.3513E-163

1.3332E-176

0

0.00742472

HHO-ADAP

1.09779E-14

0.001381129

5.07818E-06

0.007170666

0.010577027

HHO-PSO

8.9439E-83

1.65484E-60

1.91329E-64

8.09924E-60

0.016852227

HHO-Inertia

2.44743E-52

1.63736E-30

5.80459E-42

8.03011E-30

0.008446463

HHO-ULTRA

5.00297E-06

0.017311473

0.00194876

0.030510794

0.052404387

WMA

212.2599742

1328.000999

1020.625265

1090.403997

1.301981907

CMA-ES

2.82617E-37

3.59094E-36

2.58397E-36

3.23155E-36

0.243748417

EBOwithCMAR

4.3793E-16

1.76966E-11

5.9888E-13

4.78483E-11

0.283337053

L-SHADE

2.73336E-22

3.00106E-15

7.73193E-19

1.63573E-14

0.111896873

LSHADE-cnEpSin

4.06451E-42

5.7417E-34

1.86786E-39

3.14251E-33

1.258401553

SPS-L-SHADE-EIG

8.81194E-32

2.65614E-29

3.55521E-30

5.52945E-29

0.487809403

OWMA

2.71647E-18

6.87522E-16

3.49224E-16

8.90236E-16

0.390349337

F4

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

5.8888E-103

6.18914E-93

1.91521E-97

3.10127E-92

0.00385609

HHO-Elite

6.6264E-302

2.4688E-97

1.0241E-102

1.14898E-96

0.006447393

HHO-GA

7.89701E-06

0.000932747

0.000454413

0.001036913

0.003503287

HHO-CHAOS

6.1082E-105

2.06841E-94

3.67948E-98

6.36312E-94

0.002045113

HHO-ADAP

1.92594E-07

0.000151656

6.15767E-05

0.000235359

0.00499801

HHO-PSO

1.18027E-45

1.14374E-39

9.75576E-42

3.50094E-39

0.00179286

HHO-Inertia

1.56051E-38

6.2421E-34

1.14154E-35

2.07296E-33

0.001140383

HHO-ULTRA

0.000205586

0.01066

0.005769018

0.013352992

0.009947233

WMA

3.679406574

11.67034928

10.37738109

5.528059404

0.335859337

CMA-ES

6.709E-20

2.07097E-19

1.8027E-19

1.17549E-19

0.162250263

EBOwithCMAR

1.98839E-10

6.31351E-09

3.90342E-09

7.95552E-09

0.225978663

L-SHADE

8.36461E-08

7.79887E-07

6.20888E-07

6.62649E-07

0.076010597

LSHADE-cnEpSin

1.64452E-19

2.79762E-17

4.81307E-18

6.42924E-17

0.95325638

SPS-L-SHADE-EIG

1.00628E-12

8.15619E-12

7.23305E-12

5.96963E-12

0.4125385

OWMA

1.98937E-09

7.99841E-09

5.90752E-09

6.959E-09

0.28919723

F5

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

1.68835E-07

0.000828833

0.000468534

0.00093781

0.00642964

HHO-Elite

0

0.000616189

6.49304E-05

0.001050139

0.011401483

HHO-GA

6.682867017

7.24829032

7.303408877

0.277408152

0.00775861

HHO-CHAOS

1.33161E-05

0.000529628

0.000325929

0.000707741

0.007548757

HHO-ADAP

1.54125E-05

0.002680439

0.001656907

0.002939156

0.006599057

HHO-PSO

4.09502E-06

0.001382272

0.000758328

0.00171852

0.006955423

HHO-Inertia

5.67729E-07

0.001058966

0.000505681

0.001235915

0.00387482

HHO-ULTRA

2.96375E-06

0.02200018

0.003783848

0.048701382

0.013944793

WMA

1943.868232

43,434.47416

18,449.26736

67,927.68464

0.416770623

CMA-ES

0

0.13288597

8.75759E-30

0.727846436

0.195107977

EBOwithCMAR

0.006971864

1.600082797

0.809968234

1.656792613

0.25437131

L-SHADE

3.98496E-11

1.953697281

0.546457635

2.095311667

0.074911067

LSHADE-cnEpSin

0

1.55307E-30

0

7.57967E-30

0.92940832

SPS-L-SHADE-EIG

1.60566E-18

0.000279148

6.29988E-15

0.001528956

0.339157667

OWMA

8.933513986

8.969077219

8.971850862

0.014753683

0.256061313

F6

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

1.38731E-08

1.29633E-05

9.10541E-06

1.46795E-05

0.002401213

HHO-Elite

0

8.3371E-06

1.78271E-06

1.84081E-05

0.008764883

HHO-GA

2.64497E-06

4.01883E-05

1.71107E-05

4.57062E-05

0.01044252

HHO-CHAOS

1.84944E-09

2.75683E-06

7.862E-07

5.04768E-06

0.008038173

HHO-ADAP

1.59203E-06

9.58456E-05

5.01994E-05

0.000121877

0.002729547

HHO-PSO

8.20887E-08

7.85374E-06

1.8023E-06

1.90027E-05

0.002541773

HHO-Inertia

5.8901E-08

1.88156E-05

1.01919E-05

3.1222E-05

0.001283697

HHO-ULTRA

1.83785E-06

0.000775165

0.000210266

0.001323936

0.01117304

WMA

6.103165639

115.7271038

79.28185523

143.4876142

0.30629959

CMA-ES

0

0

0

0

0.11928363

EBOwithCMAR

6.16298E-33

8.75677E-30

1.05541E-30

1.91312E-29

0.16319388

L-SHADE

0

2.05433E-34

0

7.81799E-34

0.052445133

LSHADE-cnEpSin

0

3.69779E-33

0

7.69415E-33

0.79619724

SPS-L-SHADE-EIG

0

2.44465E-32

4.62223E-33

4.64656E-32

0.402029157

OWMA

1.023886666

1.791807374

1.784275648

0.271249853

0.29821969

F7

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

1.34784E-07

6.30425E-05

4.92781E-05

6.25298E-05

0.00642125

HHO-Elite

8.72074E-07

7.01869E-05

3.1554E-05

8.47253E-05

0.01551028

HHO-GA

7.96258E-05

0.000858307

0.000841714

0.00048836

0.024328017

HHO-CHAOS

1.02501E-06

6.50962E-05

4.42988E-05

6.40993E-05

0.014950727

HHO-ADAP

1.56798E-06

0.000120623

9.19094E-05

0.000139443

0.016023683

HHO-PSO

2.44533E-06

0.000100688

7.89471E-05

8.39591E-05

0.01941968

HHO-Inertia

1.90041E-06

6.25612E-05

3.60599E-05

6.95611E-05

0.01108321

HHO-ULTRA

1.72666E-06

8.89047E-05

4.63282E-05

0.000116096

0.017277727

WMA

0.00353242

0.077361034

0.063663863

0.061055252

0.412974063

CMA-ES

0.001467285

0.00602014

0.004989935

0.002979487

0.210737753

EBOwithCMAR

0.000574634

0.001885765

0.001899759

0.000870145

0.239214547

L-SHADE

0.000335629

0.001616039

0.001597911

0.000776146

0.081023623

LSHADE-cnEpSin

0.000157329

0.001322506

0.001427638

0.000498462

0.785694747

SPS-L-SHADE-EIG

0.000533397

0.002635231

0.002520453

0.001349827

0.322179073

OWMA

3.52887E-05

0.002672107

0.002084125

0.0021053

0.3967357