Table 6 Test result of unimodal benchmark functions with dim = 50.

HHO

9.3401E-206

4.9397E-181

6.1065E-195

0

0.002614573

HHO-Elite

0

1.282E-192

1.8361E-203

0

0.007671367

HHO-GA

59.30202369

398.0512192

353.6136417

203.8391134

0.005033433

HHO-CHAOS

8.3034E-202

3.1327E-186

4.9628E-196

0

0.002574377

HHO-ADAP

1.19785E-87

2.14629E-60

1.84599E-70

1.16977E-59

0.004451813

HHO-PSO

4.70499E-97

7.23113E-77

1.49206E-81

3.65408E-76

0.002123527

HHO-Inertia

6.53943E-74

7.30211E-66

2.31809E-68

1.83482E-65

0.001127

HHO-ULTRA

4.80337E-11

0.00269131

0.000172278

0.006933796

0.012548357

WMA

2388.08418

6454.390494

5862.742004

2548.958802

0.27554816

CMA-ES

1.27372E-08

1.96939E-08

1.83367E-08

6.31761E-09

0.319487947

EBOwithCMAR

0.016177033

2.096761903

0.351179634

6.751875196

0.35987825

L-SHADE

7.4221E-09

0.000367036

2.75507E-06

0.001810368

0.061966603

LSHADE-cnEpSin

2.43138E-20

2.95434E-19

1.85293E-19

4.87383E-19

81.90702328

SPS-L-SHADE-EIG

1.18139E-09

4.04054E-08

1.96541E-08

7.83725E-08

4.13770014

OWMA

4.33622E-17

1.24236E-15

8.96232E-16

1.11249E-15

2.038484233

F2

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

1.2766E-105

2.39705E-96

5.2538E-100

1.04515E-95

0.003263743

HHO-Elite

1.6323E-110

9.6912E-99

9.9732E-105

3.53181E-98

0.04764154

HHO-GA

3.44409251

7.189650544

7.44108858

1.945104928

0.00637425

HHO-CHAOS

1.1842E-101

1.12622E-92

1.42063E-97

5.76779E-92

0.003603347

HHO-ADAP

8.779E-62

5.23315E-51

7.11504E-56

2.57911E-50

0.00475963

HHO-PSO

2.6723E-47

2.21725E-40

4.45627E-41

6.49074E-40

0.002669997

HHO-Inertia

1.58841E-39

2.94186E-34

5.69287E-35

8.08691E-34

0.00197438

HHO-ULTRA

5.89801E-08

0.015894708

0.006265289

0.02286062

0.01535147

WMA

47.31217724

671,089.523

111.6626543

3,674,336.716

0.28150155

CMA-ES

0.000234099

0.000349629

0.000331887

8.09659E-05

0.338791633

EBOwithCMAR

0.022866662

0.61789428

0.145328274

1.818174778

0.38463833

L-SHADE

6.50737E-06

0.000446284

8.99666E-05

0.001045109

0.068226973

LSHADE-cnEpSin

3.31413E-09

1.0537E-08

9.61269E-09

5.20386E-09

37.17167179

SPS-L-SHADE-EIG

9.03809E-06

5.46547E-05

3.15575E-05

5.18289E-05

1.72442401

OWMA

3.64936E-09

1.3217E-08

1.14457E-08

7.81532E-09

1.070093457

F3

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

1.8279E-187

3.3249E-127

3.9259E-161

1.8211E-126

0.065147347

HHO-Elite

1.7144E-190

7.332E-148

3.2626E-166

4.0095E-147

0.111250407

HHO-GA

3064.218046

5999.442965

5983.45995

2166.058313

0.091116443

HHO-CHAOS

4.9044E-178

3.0244E-147

4.1112E-163

1.6331E-146

0.05172383

HHO-ADAP

3.25102E-07

1.272479364

0.087495184

3.599771352

0.06492744

HHO-PSO

3.20191E-59

1.6756E-42

5.0738E-50

7.6304E-42

0.068722223

HHO-Inertia

5.45029E-28

1.67222E-16

7.96019E-22

8.53331E-16

0.034483747

HHO-ULTRA

7.04756E-07

3.302794852

0.355613631

8.825665964

0.054232727

WMA

15,400.02346

57,656.50038

33,774.12379

68,001.65223

0.586689137

CMA-ES

5.484391678

50.56445641

21.43394315

80.16154573

0.608205753

EBOwithCMAR

12,705.85048

25,155.02645

24,967.45223

5983.026482

0.503807067

L-SHADE

544.5971517

1687.283516

1351.006562

1213.241445

0.214647183

LSHADE-cnEpSin

1.3263E-05

0.000461491

0.000283339

0.000520432

29.81959852

SPS-L-SHADE-EIG

119.3058584

345.1980773

318.9433598

154.1272228

1.99567374

OWMA

4.11236E-16

1.88926E-14

6.49453E-15

3.127E-14

1.654590233

F4

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

2.4715E-106

4.50388E-92

2.02776E-97

2.45964E-91

0.00360151

HHO-Elite

4.5864E-269

3.31964E-96

9.1051E-102

1.78302E-95

0.008252207

HHO-GA

4.936655714

8.572640236

8.550167845

1.842650104

0.004395533

HHO-CHAOS

3.3064E-105

4.29601E-94

3.84617E-98

2.31983E-93

0.002823987

HHO-ADAP

6.37625E-08

0.000198342

1.04197E-05

0.000490289

0.01374998

HHO-PSO

5.31722E-48

4.88331E-39

1.14674E-42

2.08414E-38

0.004548463

HHO-Inertia

3.83042E-39

5.07042E-33

1.01052E-34

1.31163E-32

0.003508353

HHO-ULTRA

0.000117754

0.007444848

0.003352918

0.010146496

0.04565488

WMA

20.36591194

35.55881021

35.48712921

6.587163028

1.222124453

CMA-ES

0.333283251

94.63145163

98.52677701

17.92478308

0.932492763

EBOwithCMAR

20.05225087

33.06159554

32.22600772

8.138841856

1.01696359

L-SHADE

7.45352717

10.58073797

10.34988825

2.196688336

0.291803773

LSHADE-cnEpSin

0.00171199

0.003703834

0.003403832

0.001622869

40.92281143

SPS-L-SHADE-EIG

3.409486258

9.50724688

8.923982017

2.638393334

1.388597003

OWMA

4.48257E-09

1.4236E-08

1.41088E-08

7.1582E-09

0.996567367

F5

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

4.57772E-06

0.005005628

0.002267289

0.007217424

0.020499137

HHO-Elite

0

0.002158316

4.50213E-05

0.00469344

0.029099967

HHO-GA

1421.406503

15,638.95346

11,331.81332

11,038.62853

0.02407007

HHO-CHAOS

8.9854E-06

0.001891152

0.001261376

0.001799051

0.016782337

HHO-ADAP

5.34653E-05

0.017013986

0.005305222

0.019896059

0.02281945

HHO-PSO

0.000142044

0.006320066

0.002675313

0.010419643

0.013529967

HHO-Inertia

2.13573E-07

0.005523574

0.001195322

0.010248518

0.008043113

HHO-ULTRA

3.57496E-05

0.085536556

0.005756505

0.164548196

0.054837427

WMA

1,038,336.73

3,914,265.286

2,806,657.877

2,915,405.654

1.454739637

CMA-ES

39.55411789

54.55134115

41.00458512

30.70250841

0.97113546

EBOwithCMAR

211.4331729

691.8966328

556.006668

532.2545694

0.449478867

L-SHADE

42.14059603

187.6423584

177.1882102

80.50401985

0.076721477

LSHADE-cnEpSin

38.6260978

39.68380278

39.53678078

0.865111202

23.83702145

SPS-L-SHADE-EIG

30.45979706

77.24919029

85.54634098

33.59897311

0.723851493

OWMA

48.89220055

48.96653685

48.96949047

0.020909908

0.290208873

F6

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

1.36345E-07

6.50905E-05

2.5027E-05

8.92637E-05

0.00490366

HHO-Elite

6.67766E-14

7.76737E-05

1.52735E-05

0.00013194

0.033822063

HHO-GA

129.826706

399.0753826

406.7957714

178.9279079

0.011760673

HHO-CHAOS

1.55865E-08

4.6443E-05

1.45428E-05

6.5125E-05

0.010756307

HHO-ADAP

1.20669E-07

0.000393542

0.000264869

0.000385638

0.016242173

HHO-PSO

4.26864E-07

4.51459E-05

2.52833E-05

6.09962E-05

0.00674214

HHO-Inertia

5.75672E-08

0.000125486

3.67317E-05

0.000216774

0.004236167

HHO-ULTRA

6.04855E-07

0.003126471

0.00062447

0.005397723

0.04643525

WMA

3356.311339

6832.179603

6369.223112

2145.898502

1.415256407

CMA-ES

9.56616E-09

2.185E-08

2.09231E-08

7.56149E-09

0.872574897

EBOwithCMAR

0.014804503

0.313109423

0.143646747

0.503261964

0.976461043

L-SHADE

5.09055E-09

0.00190447

5.26985E-06

0.009642412

0.319020223

LSHADE-cnEpSin

1.43318E-20

1.34685E-19

9.85653E-20

1.14093E-19

51.09293181

SPS-L-SHADE-EIG

1.80423E-09

2.76163E-08

1.102E-08

3.89763E-08

1.686763383

OWMA

10.56627192

11.75791219

11.81471111

0.39877868

0.651474177

F7

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

3.80311E-06

0.000105211

5.46419E-05

0.000195123

0.020717163

HHO-Elite

8.46535E-07

7.58061E-05

4.87507E-05

8.56838E-05

0.080874423

HHO-GA

0.010732345

0.078582692

0.070152354

0.043812433

0.058166727

HHO-CHAOS

2.95436E-07

9.44456E-05

7.58558E-05

9.49373E-05

0.019083043

HHO-ADAP

3.42179E-06

0.000207325

8.91345E-05

0.000325382

0.042578507

HHO-PSO

3.16772E-06

0.000146392

0.000101147

0.000158603

0.060131127

HHO-Inertia

3.89171E-06

0.000112884

9.11148E-05

0.000116133

0.02562542

HHO-ULTRA

1.52863E-06

0.000284233

0.000101202

0.000447001

0.117736113

WMA

4.728919751

17.09635618

16.87189686

7.052113736

1.694395367

CMA-ES

0.031903991

0.053489901

0.052505121

0.011110853

1.21721709

EBOwithCMAR

0.141878093

0.301189157

0.317841127

0.132091394

1.216524583

L-SHADE

0.062211569

0.172095778

0.143373969

0.110385883

0.22274802

LSHADE-cnEpSin

0.001648779

0.002889394

0.002961601

0.000807443

46.54748303

SPS-L-SHADE-EIG

0.025615702

0.06406911

0.068681736

0.01797735

1.72884909

OWMA

1.56053E-05

0.001947872

0.001548717

0.001406308

1.557339993