Table 6 GD, Spacing, and Spread metrics for algorithms on ZDT1, ZDT2, ZDT3, and ZDT6 test functions.

From: An efficient multi-objective parrot optimizer for global and engineering optimization problems

Algorithm

GD

Spacing

Spread

Mean

SD

Mean

SD

Mean

SD

ZDT1

MOPSO

0.0169

0.0009

0.0102

0.0022

0.7864

0.0384

NSGA-II

0.0362

0.0012

0.0111

0.0010

0.6468

0.0340

MOGWO

0.0227

0.0020

0.0240

0.0066

1.0308

0.0864

MOWOA

0.0170

0.0061

0.0367

0.0162

1.2024

0.0934

MOSMA

0.0199

0.0023

0.0134

0.0032

0.7989

0.1624

IMOMRFO

0.0210

0.0019

0.0158

0.0036

0.7948

0.0591

MOGTO

0.0207

0.0004

0.0110

0.0011

0.6716

0.0534

MOPO

0.0155

0.0004

0.0074

0.0006

0.5858

0.0496

ZDT2

MOPSO

0.0127

0.0010

0.0118

0.0018

1.0182

0.0384

NSGA-II

0.0411

0.0016

0.0095

0.0011

0.8390

0.0390

MOGWO

0.0014

0.0005

0.0252

0.0070

1.0405

0.0748

MOWOA

0.0009

0.0018

0.0377

0.0134

1.2256

0.1401

MOSMA

0.0008

0.0003

0.0141

0.0013

0.6289

0.1016

IMOMRFO

0.0157

0.0039

0.0246

0.0092

1.0168

0.0592

MOGTO

0.0001

0.0001

0.0122

0.0013

0.4235

0.0443

MOPO

0.0001

0.0001

0.0086

0.0009

0.5597

0.0938

ZDT3

MOPSO

0.1471

0.0095

0.0540

0.0193

0.8124

0.0291

NSGA-II

0.2749

0.0221

0.0243

0.0036

0.8045

0.0367

MOGWO

0.1554

0.0890

0.3332

0.1904

1.0405

0.2072

MOWOA

0.2746

0.2628

0.1685

0.0880

0.8551

0.1449

MOSMA

0.0076

0.0023

0.0429

0.0087

1.0815

0.1540

IMOMRFO

0.7389

0.1966

0.2266

0.1359

0.8848

0.0626

MOGTO

0.0005

0.0004

0.0389

0.0365

0.7421

0.2700

MOPO

0.0002

0.0000

0.0132

0.0006

0.7550

0.0972

ZDT6

MOPSO

5.5101

4.6479

0.2827

0.3404

0.9385

0.1266

NSGA-II

4.1147

0.8008

0.5229

0.4140

1.2641

0.1916

MOGWO

4.3840

3.2942

0.8561

0.6238

1.1644

0.2132

MOWOA

4.2619

2.4773

0.7543

0.8167

1.3316

0.2093

MOSMA

2.4718

0.8532

1.9221

0.7057

1.3349

0.3132

IMOMRFO

2.1858

1.3401

1.8867

1.8246

1.4996

0.3513

MOGTO

3.3656

0.4054

2.3782

1.2591

1.6145

0.1913

MOPO

1.7742

1.0307

0.3543

0.4001

1.2542

0.2332

  1. Significant values are in (bold).