Table 7 Test result of unimodal benchmark functions with dim = 100.

HHO

1.2837E-211

4.4315E-183

2.9184E-195

0

0.003946797

HHO-Elite

2.1038E-216

2.2331E-188

1.7758E-202

0

0.008829393

HHO-GA

2251.406289

5124.414774

4892.495265

1492.465624

0.00724302

HHO-CHAOS

1.7141E-206

2.449E-183

2.4115E-193

0

0.003929183

HHO-ADAP

1.77699E-78

2.28238E-65

3.85851E-70

1.23373E-64

0.00659185

HHO-PSO

1.2658E-87

9.44326E-76

9.87305E-81

5.13077E-75

0.0021907

HHO-Inertia

8.72639E-72

2.83925E-65

1.19574E-67

9.01902E-65

0.001544343

HHO-ULTRA

7.82734E-09

0.005295998

0.000469742

0.012973966

0.0173669

WMA

10,846.50567

16,428.35247

15,442.0986

5113.147338

0.313357717

CMA-ES

0.002804268

0.004872848

0.004954762

0.000914862

0.876947917

EBOwithCMAR

282.7353489

1405.830178

1180.592069

941.3728374

0.88215096

L-SHADE

0.105375349

17.00521638

7.294712784

26.13415042

0.078803227

LSHADE-cnEpSin

4.72408E-11

1.53493E-10

1.4898E-10

7.33473E-11

2.27017099

SPS-L-SHADE-EIG

0.008688195

0.069066271

0.048425899

0.055990594

1.48449032

OWMA

1.07709E-16

3.26248E-15

1.59955E-15

3.83459E-15

0.327800147

F2

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

4.8525E-109

1.7615E-95

1.4384E-100

9.07812E-95

0.003886167

HHO-Elite

1.3303E-254

3.0959E-99

3.3989E-103

1.46783E-98

0.009280537

HHO-GA

12.22549127

34.94933074

36.56199201

6.770620961

0.007522073

HHO-CHAOS

9.9567E-104

1.13326E-93

6.9712E-99

5.10844E-93

0.004440063

HHO-ADAP

1.43745E-68

5.86558E-52

6.24972E-56

3.15271E-51

0.00310493

HHO-PSO

7.21724E-47

1.47409E-39

1.9506E-41

5.89407E-39

0.00297178

HHO-Inertia

1.03388E-37

9.76512E-34

1.34832E-34

2.04657E-33

0.002467067

HHO-ULTRA

6.59988E-06

0.046510446

0.01098697

0.067767931

0.018660667

WMA

127.5672806

2.98851E + 14

201.9572327

1.6367E + 15

0.317677603

CMA-ES

0.166033431

0.248881785

0.247989328

0.0422668

0.886822267

EBOwithCMAR

6.981309953

22.7182028

21.69346394

9.572123623

0.890721527

L-SHADE

0.094744884

1.360108499

0.988797057

1.23581945

0.082553387

LSHADE-cnEpSin

4.04442E-05

0.000101464

9.36297E-05

5.11794E-05

2.387489497

SPS-L-SHADE-EIG

0.047173412

0.165368167

0.143348631

0.104147627

2.363582173

OWMA

1.67876E-08

4.72629E-08

4.12467E-08

2.41896E-08

1.156558473

F3

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

4.7748E-176

3.6877E-121

6.1471E-146

2.0128E-120

0.049762267

HHO-Elite

1.338E-180

7.9957E-110

3.9325E-154

4.3794E-109

0.077010573

HHO-GA

17,807.2348

69,403.0382

69,518.53758

16,176.17325

0.072268293

HHO-CHAOS

1.2395E-178

1.4598E-140

4.3355E-155

7.9957E-140

0.040101167

HHO-ADAP

0.003148191

14.73225432

2.37261849

36.78705714

0.059618497

HHO-PSO

2.68465E-56

1.86567E-34

1.80386E-46

1.02157E-33

0.062100513

HHO-Inertia

6.6921E-27

7.28301E-12

6.41166E-17

2.62896E-11

0.025459597

HHO-ULTRA

7.1951E-06

26.83736169

3.67613297

68.87636163

0.091872367

WMA

84,108.97124

518,821.9116

305,972.5989

465,614.6115

0.90847512

CMA-ES

205,089.5395

390,687.2494

367,373.9277

113,597.3984

1.58057413

EBOwithCMAR

106,857.2542

150,961.2524

139,391.4024

32,421.0569

1.311145717

L-SHADE

10,795.8657

17,225.82719

15,968.84892

5988.036648

0.385066633

LSHADE-cnEpSin

11.87630887

28.4105277

28.01723394

9.188909888

11.38464598

SPS-L-SHADE-EIG

2626.277808

5120.00171

4833.627573

1902.02804

1.839042813

OWMA

2.0386E-15

5.40633E-14

2.23712E-14

1.0427E-13

0.91878421

F4

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

3.5218E-102

2.68844E-91

7.25973E-97

1.02256E-90

0.005977993

HHO-Elite

8.9442E-295

4.10232E-95

4.5827E-100

1.94625E-94

0.01083807

HHO-GA

18.40446943

31.16526385

31.66381079

4.499315046

0.007202573

HHO-CHAOS

1.9655E-103

4.0933E-94

4.03875E-98

1.71528E-93

0.004376777

HHO-ADAP

8.82421E-07

0.000183933

5.23521E-05

0.000317484

0.009584113

HHO-PSO

1.42403E-47

2.2538E-39

1.39351E-41

7.3198E-39

0.003205473

HHO-Inertia

2.08879E-38

1.76865E-32

1.84542E-34

8.04461E-32

0.001857387

HHO-ULTRA

0.000115732

0.010744839

0.00858357

0.010899722

0.018675707

WMA

31.5886922

47.86576676

48.09302578

9.049752321

0.313438867

CMA-ES

97.04836683

99.20363416

99.37355488

0.67750444

0.877692007

EBOwithCMAR

39.27839424

59.85683636

59.41784594

9.779385511

0.838153543

L-SHADE

18.47480251

33.82092083

31.38747446

10.28118013

0.074501113

LSHADE-cnEpSin

0.276009375

0.404290018

0.368949178

0.103663444

2.278696017

SPS-L-SHADE-EIG

17.02038701

21.3796043

20.59538603

3.131173308

1.464883417

OWMA

3.81582E-09

1.27407E-08

9.87418E-09

9.79251E-09

0.325740247

F5

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

9.52024E-05

0.015078921

0.002916138

0.02830839

0.010788657

HHO-Elite

0

0.004478769

0.000278975

0.007105732

0.015509887

HHO-GA

159,230.2181

1,889,607.104

1,756,697.258

1,028,736.257

0.008978433

HHO-CHAOS

4.63988E-05

0.003882829

0.002270472

0.004432184

0.00807254

HHO-ADAP

0.000545527

0.040564061

0.02288722

0.05780806

0.01147216

HHO-PSO

1.51351E-05

0.01720206

0.003958642

0.028719484

0.00545623

HHO-Inertia

1.24061E-06

0.009415769

0.003467055

0.017024993

0.00382287

HHO-ULTRA

3.11404E-05

0.160761858

0.038745275

0.337018506

0.021248803

WMA

2,837,219.309

10,070,124.51

10,080,291.09

4,154,688.4

0.34624518

CMA-ES

95.694239

129.8429989

97.73349397

62.04159964

0.910853047

EBOwithCMAR

98,539.5981

2,353,066.978

779,376.2468

4,413,713.73

0.89889107

L-SHADE

839.4206189

16,389.46211

3888.122492

36,633.12715

0.095708997

LSHADE-cnEpSin

90.82622131

91.87491108

91.55543007

1.034227065

2.689202857

SPS-L-SHADE-EIG

283.0638641

525.6124515

506.393659

117.9038711

4.293254963

OWMA

98.93005775

98.96813831

98.97093456

0.016912765

0.86304991

F6

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

4.26507E-07

9.12472E-05

4.8542E-05

0.000123505

0.007318267

HHO-Elite

3.52617E-25

0.000110655

1.96445E-05

0.000198421

0.036224943

HHO-GA

3126.125639

5476.429861

5303.639

1584.072988

0.01708462

HHO-CHAOS

1.12286E-07

8.97418E-05

2.88621E-05

0.000146463

0.01201278

HHO-ADAP

4.69591E-07

0.001847804

0.000838597

0.00225389

0.018537163

HHO-PSO

3.15132E-08

0.000111834

5.70387E-05

0.000142821

0.00698113

HHO-Inertia

4.02544E-08

0.000153528

4.52027E-05

0.000217878

0.00530771

HHO-ULTRA

7.45501E-05

0.003931442

0.001202519

0.005735587

0.057630337

WMA

2958.447925

15,242.13278

14,820.09247

4905.934585

1.245651437

CMA-ES

0.00320299

0.00480043

0.004894476

0.000834777

3.200690983

EBOwithCMAR

273.9488306

1319.526072

1086.191473

1061.725654

2.951521947

L-SHADE

0.187632351

14.64304642

5.45678175

23.72128509

0.256597603

LSHADE-cnEpSin

2.82574E-11

1.96218E-10

1.76032E-10

1.20228E-10

8.122864587

SPS-L-SHADE-EIG

0.010606627

0.055879542

0.04089426

0.04133879

4.271833143

OWMA

22.02145797

24.20047015

24.31062756

0.562675311

1.227214983

F7

Algorithm

Best

Mean

Median

Standard deviation

Average Time Per Run (sec.)

HHO

6.32716E-06

9.73989E-05

7.42113E-05

0.000109421

0.068673407

HHO-Elite

2.83854E-06

9.7451E-05

8.65198E-05

8.77353E-05

0.10561249

HHO-GA

0.582766688

2.839690369

2.681262174

1.288229335

0.08985718

HHO-CHAOS

7.14024E-06

8.08573E-05

8.36449E-05

5.62775E-05

0.064391867

HHO-ADAP

1.83232E-06

0.000381361

0.000134122

0.000746189

0.063380327

HHO-PSO

1.28306E-05

9.30517E-05

5.53446E-05

8.4323E-05

0.078562893

HHO-Inertia

4.54299E-06

9.52401E-05

6.39134E-05

0.000107481

0.03719595

HHO-ULTRA

2.88872E-06

0.000143993

8.1196E-05

0.000155978

0.13484015

WMA

14.46243926

76.9454062

76.11049483

35.91926185

1.863829383

CMA-ES

0.090020901

0.145899764

0.149637552

0.020848735

3.718241993

EBOwithCMAR

1.262465944

5.963733265

4.292127752

3.830484939

3.16689422

L-SHADE

0.622147667

1.378375549

1.327464237

0.494897517

0.58929098

LSHADE-cnEpSin

0.001817597

0.004099756

0.004034475

0.001089424

17.86593315

SPS-L-SHADE-EIG

0.21608724

0.412893938

0.383942706

0.138996254

2.17114854

OWMA

1.49421E-05

0.001238768

0.000804351

0.001298953

0.740818283