Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems

Table 15

Results for LDIW-PSO and 𝐿-PSO_CLUS for the 7 nonscaled benchmark problems.

Problem

Booth

Easom

Michalewicz

Schaffer's f6

Salomon

Shubert

Trid-6

Algorithm

LDIW-PSO

𝐿-PSOCLUS

LDIW-PSO

𝐿-PSOCLUS

LDIW-PSO

𝐿-PSOCLUS

LDIW-PSO

𝐿-PSOCLUS

LDIW-PSO

𝐿-PSOCLUS

LDIW-PSO

𝐿-PSOCLUS

LDIW-PSO

𝐿-PSOCLUS

Best fitness

0.0000𝑒+00

0.0000𝑒+00

−1.0000𝑒+00

−1.0000𝑒+00

−3.4792𝑒+00

−𝟒.𝟑𝟕𝟔𝟐𝐞+𝟎𝟎

0.0000𝑒+00

0.0000𝑒+00

9.9833𝑒−02

𝟑.𝟑𝟏𝟖𝟗𝐞−𝟔𝟓

−1.8673𝑒+02

−1.8673𝑒+02

−5.0000𝑒+01

−5.0000𝑒+01

Mean fitness

0.0000𝑒+00

0.0000𝑒+00

−1.0000𝑒+00

−1.0000𝑒+00

−2.6736𝑒+00

−𝟒.𝟏𝟎𝟓𝟔𝐞+𝟎𝟎

1.5545𝑒−03

𝟏.𝟏𝟔𝟓𝟗𝐞−𝟎𝟑

9.9833𝑒−02

𝟖.𝟕𝟖𝟓𝟑𝐞−𝟎𝟐

−1.8673𝑒+02

−1.8673𝑒+02

−50000𝑒+01

−50000𝑒+01

Std. Dev.

0.0000𝑒+00

0.0000𝑒+00

6.6613𝑒−16

6.6613𝑒−16

3.6921𝑒−01

𝟏.𝟔𝟏𝟗𝟔𝐞−𝟎𝟏

3.5619𝑒−03

𝟑.𝟏𝟓𝟕𝟑𝐞−𝟎𝟑

𝟕.𝟑𝟒𝟑𝟒𝐞−𝟏𝟖

3.2442𝑒−02

𝟑.𝟗𝟑𝟖𝟐𝐞−𝟏𝟒

7.5559𝑒−05

𝟕.𝟖𝟓𝟕𝟐𝐞−𝟏𝟒

9.3154𝑒−14

Av. iteration

79.48

81.16

107.16

73.12

—

—

279.90

174.14

—

742

175.52

208.20

287.48

281.72

SR (%)

100

100

100

100

0

0

84

88

0

12

100

96

100

100