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Artificial bee colony algorithm including some components of iterated greedy algorithm for permutation flow shop scheduling problems

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Abstract

The permutation flow shop scheduling problem has been investigated by researchers for more than 40 years due to its complexity and lots of real-life examples of the problem. Many exact or approximate solution approaches have been presented for the problem. Among solution approaches in the literature, iterated greedy algorithm and its variants are the most effective solution methods for the problem. This paper proposes a hybrid solution algorithm that uses the best components such as local search operators and destruction/construction operators of the variants of iterated greedy algorithm in an artificial bee colony algorithm. An ANOVA is made for determining the most proper components of iterated greedy algorithm. Then, these components are combined with artificial bee colony algorithm. Furthermore, a design of experiment is made for determining the best parameter setting for the proposed hybrid artificial bee colony. The experimental results of the proposed algorithm compared with variants of iterated greedy algorithms in the literature show that the proposed algorithm produces better solutions that deviate less from the optimum or lower-bound solutions for permutation flow shop scheduling problems with the makespan performance criterion.

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Author information

Authors and Affiliations

  1. Industrial Engineering Department, Nuh Naci Yazgan University, 38170, Kayseri, Turkey

    Oğuzhan Ahmet Arık

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  1. Oğuzhan Ahmet Arık
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Correspondence to Oğuzhan Ahmet Arık.

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Appendices

Appendices

1.1 Appendix 1: Main effects plot for ARPD values of IG variants for Taillard’s test instances

figure h

1.2 Appendix 2: Tukey procedure for local search mechanism for partial solution

figure i

1.3 Appendix 3: Tukey procedure for destruction/construction type

figure j

1.4 Appendix 4: Tukey procedure for local search mechanism for complete solution

figure k

1.5 Appendix 5: Detailed ARPD values of algorithms (t = 30)

n

m

NONE_DC_LS

NONE_DC_RIS

PLS_DC_LS

PLS_DC_RIS

PRIS_DC_LS

PRIS_DC_RIS

NONE_eDC_LS

NONE_eDC_RIS

PLS_eDC_LS

PLS_eDC_RIS

PRIS_eDC_LS

PRIS_eDC_RIS

ABC

20

5

0.0389

0.0324

0.0405

0.0324

0.0405

0.0405

0.0243

0.0243

0.0324

0.0324

0.0405

0.0243

0.0405

 

10

0.0393

0.0441

0.0325

0.0378

0.0365

0.0221

0.0250

0.0156

0.0183

0.0273

0.0351

0.0208

0.0248

 

20

0.0709

0.0674

0.0406

0.0201

0.0202

0.0124

0.0282

0.0406

0.0170

0.0211

0.0328

0.0257

0.0123

50

5

0.0063

0.0071

0.0056

0.0028

0.0042

0.0000

0.0056

0.0028

0.0028

0.0021

0.0000

0.0056

0.0000

 

10

0.5464

0.5382

0.4758

0.4969

0.5076

0.5267

0.5097

0.5110

0.5407

0.5009

0.4837

0.5456

0.4431

 

20

0.9538

0.9416

0.8029

0.8898

0.8621

0.8232

0.8526

0.8281

0.8399

0.8214

0.8825

0.8257

0.7410

100

5

0.0027

0.0000

0.0048

0.0058

0.0016

0.0008

0.0016

0.0044

0.0032

0.0044

0.0012

0.0024

0.0000

 

10

0.1590

0.1666

0.1118

0.1593

0.1215

0.1017

0.1544

0.1464

0.1200

0.1185

0.1349

0.1183

0.0639

 

20

1.2410

1.2531

1.1097

1.1800

1.1925

1.1228

1.1220

1.2306

1.1683

1.1578

1.1056

1.1438

0.9883

200

10

0.0801

0.0728

0.0578

0.0509

0.0509

0.0466

0.0616

0.0543

0.0456

0.0507

0.0451

0.0494

0.0409

 

20

1.1596

1.1915

1.0213

1.1660

1.0500

1.0768

1.1427

1.1139

1.0506

1.1109

1.0859

1.0512

0.9187

500

20

0.4525

0.4695

0.4104

0.4383

0.4517

0.4361

0.4586

0.4406

0.4422

0.4225

0.4098

0.4578

0.4241

 

Average

0.3959

0.3987

0.3428

0.3734

0.3616

0.3508

0.3655

0.3677

0.3568

0.3558

0.3548

0.3559

0.3081

1.6 Appendix 6: Detailed ARPD values of algorithms (t = 60)

n

m

NONE_DC_LS

NONE_DC_RIS

PLS_DC_LS

PLS_DC_RIS

PRIS_DC_LS

PRIS_DC_RIS

NONE_eDC_LS

NONE_eDC_RIS

PLS_eDC_LS

PLS_eDC_RIS

PRIS_eDC_LS

PRIS_eDC_RIS

ABC

20

5

0.0243

0.0324

0.0324

0.0324

0.0243

0.0243

0.0324

0.0405

0.0405

0.0324

0.0324

0.0405

0.0000

 

10

0.0393

0.0353

0.0235

0.0286

0.0338

0.0195

0.0078

0.0065

0.0260

0.0221

0.0130

0.0130

0.0143

 

20

0.0345

0.0365

0.0143

0.0052

0.0061

0.0053

0.0158

0.0141

0.0080

0.0070

0.0027

0.0000

0.0026

50

5

0.0028

0.0056

0.0028

0.0014

0.0014

0.0000

0.0056

0.0014

0.0014

0.0042

0.0014

0.0014

0.0000

 

10

0.4219

0.4080

0.4561

0.4251

0.4262

0.4140

0.4235

0.4380

0.4108

0.4579

0.4194

0.4730

0.4151

 

20

0.8083

0.7864

0.7120

0.7349

0.7062

0.6720

0.7240

0.7844

0.7115

0.7581

0.6842

0.7152

0.6453

100

5

0.0028

0.0000

0.0000

0.0000

0.0000

0.0012

0.0000

0.0000

0.0000

0.0016

0.0000

0.0000

0.0000

 

10

0.1244

0.1386

0.0733

0.0916

0.0711

0.1054

0.1211

0.1139

0.1012

0.1139

0.0739

0.0809

0.0409

 

20

1.0281

1.0148

0.9704

0.9936

0.9504

0.9668

0.9968

0.9696

0.9774

1.0060

0.9857

0.9934

0.8667

200

10

0.0614

0.0552

0.0396

0.0400

0.0388

0.0425

0.0494

0.0533

0.0427

0.0418

0.0398

0.0420

0.0391

 

20

1.0040

1.0405

0.9259

0.9400

0.9575

0.9524

0.9905

1.0048

0.9252

0.9815

0.9127

0.9191

0.8407

500

20

0.3836

0.3966

0.3775

0.3705

0.3732

0.3757

0.3950

0.4091

0.3688

0.3740

0.3781

0.3819

0.3328

 

Average

0.3280

0.3292

0.3023

0.3053

0.2991

0.2983

0.3135

0.3196

0.3011

0.3167

0.2953

0.3050

0.2665

1.7 Appendix 7: Detailed ARPD values of algorithms (t = 90)

n

m

NONE_DC_LS

NONE_DC_RIS

PLS_DC_LS

PLS_DC_RIS

PRIS_DC_LS

PRIS_DC_RIS

NONE_eDC_LS

NONE_eDC_RIS

PLS_eDC_LS

PLS_eDC_RIS

PRIS_eDC_LS

PRIS_eDC_RIS

ABC

20

5

0.0162

0.0324

0.0243

0.0162

0.0162

0.0243

0.0243

0.0243

0.0243

0.0405

0.0324

0.0243

0.0000

 

10

0.0065

0.0221

0.0260

0.0130

0.0130

0.0065

0.0065

0.0000

0.0195

0.0130

0.0260

0.0143

0.0130

 

20

0.0299

0.0327

0.0034

0.0052

0.0079

0.0052

0.0211

0.0156

0.0026

0.0000

0.0000

0.0000

0.0000

50

5

0.0042

0.0028

0.0014

0.0014

0.0000

0.0000

0.0042

0.0014

0.0014

0.0000

0.0000

0.0000

0.0000

 

10

0.3628

0.4157

0.4010

0.4158

0.4176

0.3988

0.3741

0.3832

0.4210

0.4200

0.4177

0.4492

0.3669

 

20

0.7782

0.7097

0.6535

0.6345

0.6111

0.6163

0.6592

0.6824

0.6753

0.6482

0.6661

0.6267

0.6407

100

5

0.0012

0.0012

0.0012

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

 

10

0.0859

0.1284

0.0865

0.0862

0.0733

0.0736

0.0919

0.0742

0.0679

0.0974

0.0642

0.0686

0.0450

 

20

0.9388

0.9039

0.9049

0.9192

0.8634

0.8944

0.8850

0.8881

0.8874

0.8936

0.8765

0.8660

0.7557

200

10

0.0538

0.0506

0.0364

0.0391

0.0402

0.0378

0.0425

0.0420

0.0392

0.0395

0.0367

0.0374

0.0340

 

20

0.9649

0.9233

0.8793

0.8741

0.8585

0.8735

0.9040

0.9107

0.8282

0.8823

0.8269

0.8707

0.7633

500

20

0.3635

0.3753

0.3264

0.3496

0.3517

0.3565

0.3500

0.3686

0.3236

0.3491

0.3253

0.3433

0.3195

 

Average

0.3005

0.2998

0.2787

0.2795

0.2711

0.2739

0.2802

0.2825

0.2742

0.2820

0.2727

0.2750

0.2448

1.8 Appendix 8: Detailed ARPD values of algorithms (t = 120)

n

m

NONE_DC_LS

NONE_DC_RIS

PLS_DC_LS

PLS_DC_RIS

PRIS_DC_LS

PRIS_DC_RIS

NONE_eDC_LS

NONE_eDC_RIS

PLS_eDC_LS

PLS_eDC_RIS

PRIS_eDC_LS

PRIS_eDC_RIS

ABC

20

5

0.0000

0.0162

0.0162

0.0081

0.0324

0.0243

0.0162

0.0243

0.0162

0.0162

0.0162

0.0324

0.0081

 

10

0.0195

0.0260

0.0195

0.0195

0.0130

0.0065

0.0065

0.0000

0.0195

0.0065

0.0000

0.0130

0.0065

 

20

0.0237

0.0220

0.0026

0.0043

0.0026

0.0070

0.0026

0.0070

0.0000

0.0000

0.0000

0.0000

0.0000

50

5

0.0000

0.0014

0.0000

0.0014

0.0000

0.0000

0.0028

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

 

10

0.3753

0.3391

0.3926

0.3970

0.3459

0.3890

0.3594

0.3704

0.3631

0.3823

0.3760

0.4086

0.3512

 

20

0.6509

0.6230

0.6158

0.5813

0.5914

0.5589

0.6489

0.6305

0.5779

0.5763

0.6191

0.5770

0.5539

100

5

0.0000

0.0016

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

 

10

0.1359

0.1148

0.0758

0.0654

0.0394

0.0500

0.0565

0.0626

0.0503

0.0618

0.0685

0.0525

0.0440

 

20

0.8828

0.8780

0.8145

0.8478

0.7793

0.8260

0.8412

0.8780

0.7849

0.8151

0.8055

0.8651

0.7438

200

10

0.0438

0.0478

0.0374

0.0385

0.0361

0.0363

0.0406

0.0386

0.0393

0.0338

0.0355

0.0356

0.0340

 

20

0.8946

0.9045

0.8309

0.8465

0.7716

0.8530

0.8679

0.8630

0.8188

0.7973

0.8092

0.8520

0.7159

500

20

0.3627

0.3712

0.3295

0.3163

0.3065

0.3302

0.3321

0.3435

0.3276

0.3257

0.3203

0.3354

0.3105

 

Average

0.2824

0.2788

0.2612

0.2605

0.2432

0.2568

0.2646

0.2682

0.2498

0.2512

0.2542

0.2643

0.2307

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Arık, O.A. Artificial bee colony algorithm including some components of iterated greedy algorithm for permutation flow shop scheduling problems. Neural Comput & Applic 33, 3469–3486 (2021). https://doi.org/10.1007/s00521-020-05174-1

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  • DOI: https://doi.org/10.1007/s00521-020-05174-1

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