The Effects of Using Chaotic Map on Improving the Performance of Multiobjective Evolutionary Algorithms

Table 7

The average results of Δ.

ZDT1

ZDT2

ZDT3

ZDT4

ZDT6

c

i

m

c

i

m

c

i

m

c

i

m

c

i

m

Baker

−0.0337

−0.0026

0.0015

0.0226

0.0310

0.0024

−0.0096

0.0069

0.0006

−0.0603

0.0343

−0.0513

0.0125

0.0024

−0.0015

Cat

0.0005

0.0017

0.0042

0.0234

−0.1021

−0.0145

−0.0019

−0.0052

0.0006

0.0277

−0.0090

−0.0148

−0.0001

−0.0002

−0.0068

Circle

−0.0325

−0.0035

−0.0064

−0.2019

−0.0632

−0.1410

−0.0052

−0.0065

0.0010

−0.0255

−0.0259

−0.0136

0.0031

−0.0020

0.0064

Cubic

−0.0047

0.0121

−0.0022

−0.0439

−0.0148

0.0361

0.0000

−0.0006

0.0031

−0.0052

−0.0279

0.0238

−0.0170

0.0054

−0.0017

Gauss

0.0121

0.0075

−0.0180

−0.1075

0.0329

−0.0711

−0.0024

−0.0032

0.0019

0.0330

−0.0214

0.0155

0.0180

0.0003

0.0064

ICMIC

0.0081

0.0092

0.0002

−0.0734

−0.0850

−0.0917

−0.0036

0.0008

−0.0054

−0.0356

−0.0497

0.0238

0.0123

0.0001

0.0085

Logistic

−0.0118

0.0076

0.0075

−0.1935

0.0239

0.0509

−0.0084

−0.0014

0.0080

0.0275

−0.0100

−0.0232

−0.0069

0.0020

0.0077

Sinusoidal

0.0149

0.0069

−0.0564

−0.1750

−0.0067

−0.2902

−0.0014

0.0029

−0.0286

−0.0390

−0.0164

−0.1945

0.0129

0.0088

−0.0488

Tent

−0.0350

0.0093

0.0016

0.0215

−0.0173

−0.0261

−0.0059

−0.0168

0.0071

−0.0761

−0.0139

0.0075

0.0125

0.0028

−0.0002

Zaslavskii

0.02307

0.0056

−0.0014

−0.0292

−0.0189

−0.0013

0.0099

0.0040

−0.0037

0.0201

−0.0056

0.0090

0.0038

0.0027

0.0084