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

Table 11

Results for RIW-PSO and 𝑅-PSO_CLUS for the 7 nonscaled benchmark problems.

Problem

Booth

Easom

Michalewicz

Schaffer's f6

Salomon

Shubert

Trid-6

Algorithm

RIW-PSO

𝑅-PSOCLUS

RIW-PSO

𝑅-PSOCLUS

RIW-PSO

𝑅-PSOCLUS

RIW-PSO

𝑅-PSOCLUS

RIW-PSO

𝑅-PSOCLUS

RIW-PSO

𝑅-PSOCLUS

RIW-PSO

𝑅-PSOCLUS

Best fitness

0.0000𝑒+00

0.0000𝑒 + 00

−1.0000𝑒+00

−1.0000𝑒+00

−3.3453𝑒+00

−𝟒.𝟒𝟑𝟕𝟏𝐞+𝟎𝟎

0.0000𝑒+00

0.0000𝑒+00

9.9833𝑒−02

𝟕.𝟑𝟔𝟎𝟖𝐞−𝟐𝟗

−1.8673𝑒+02

−1.8673𝑒+02

−5.0000𝑒+00

−5.0000𝑒+00

Mean fitness

0.0000𝑒+00

0.0000𝑒+00

−1.0000𝑒+00

−1.0000𝑒+00

−2.6034𝑒+00

−𝟒.𝟏𝟎𝟎𝟖𝐞+𝟎𝟎

4.7052𝑒−03

𝟏.𝟏𝟔𝟓𝟗𝐞−𝟎𝟑

9.9833𝑒−02

𝟕.𝟎𝟎𝟕𝟑𝐞−𝟎𝟐

−1.8673𝑒+02

−1.8673𝑒+02

−5.0000𝑒+00

−5.0000𝑒+00

Std. Dev.

0.0000𝑒+00

0.0000𝑒+00

6.6613𝑒−16

6.6613𝑒−16

4.2719𝑒−01

𝟏.𝟕𝟖𝟔𝟔𝐞−𝟎𝟏

4.8183𝑒−03

𝟑.𝟏𝟓𝟕𝟑𝐞−𝟎𝟑

𝟔.𝟐𝟎𝟔𝟑𝐞−𝟏𝟖

4.4236𝑒−02

𝟑.𝟕𝟕𝟎𝟔𝐞−𝟏𝟒

4.0594𝑒−14

8.6628𝑒−14

𝟕.𝟎𝟓𝟓𝟓𝐞−𝟏𝟒

Av. iteration

39.12

37.92

55.0

45.48

—

—

133.83

109.95

—

923.40

71.8

107.16

114.40

110.20

SR (%)

100

100

100

100

0

0

48

88

0

20

100

100

100

100