Improved Barebones Particle Swarm Optimization with Neighborhood Search and Its Application on Ship Design

Table 3

Results achieved by the nine PSO algorithms.

Algorithms

𝑓1

𝑓2

𝑓3

𝑓4

𝑓5

𝑓6

𝑓7

𝑓8

𝑓9

𝑓10

𝑓11

𝑓12

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

PSO

9.78𝐸−30

2.93𝐸+01

3.94𝐸−14

8.13𝐸−03

1.30𝐸−04

2.90𝐸+01

2.97𝐸+01

1.10𝐸+03

2.80𝐸−01

1.64𝐸−01

6.66𝐸−01

9.90𝐸+00

BPSO

3.60𝐸−87

1.84𝐸+01

1.12𝐸−14

9.86𝐸−03

5.65𝐸−05

3.38𝐸+01

2.50𝐸+01

2.13𝐸+03

1.90𝐸+00

2.95𝐸−02

7.95𝐸+00

6.07𝐸+01

UPSO

4.17𝐸−87

1.51𝐸+01

1.22𝐸−15

1.66𝐸−03

9.60𝐸+00

6.59𝐸+01

6.34𝐸+01

4.84𝐸+03

1.00𝐸+00

7.76𝐸−02

2.61𝐸+00

1.52𝐸+01

FIPS

2.69𝐸−12

2.45𝐸+01

4.81𝐸−07

1.16𝐸−06

1.54𝐸−01

7.30𝐸+01

6.08𝐸+01

2.05𝐸+03

2.25𝐸−15

1.70𝐸−01

5.93𝐸−14

1.20𝐸+01

CPSO-H

1.16𝐸−113

7.08𝐸+00

4.93𝐸−14

3.63𝐸−02

7.82𝐸−15

𝟎.𝟎𝟎𝐄+𝟎𝟎

1.00𝐸−01

1.08𝐸+03

1.36𝐸+00

1.20𝐸−01

4.35𝐸+00

2.67𝐸+01

CLPSO

1.46𝐸−14

2.01𝐸+01

𝟎.𝟎𝟎𝐄+𝟎𝟎

3.14𝐸−10

3.45𝐸−07

4.85𝐸−10

4.36𝐸−10

𝟏.𝟐𝟕𝐄−𝟏𝟐

3.65𝐸−05

4.50𝐸−02

3.72𝐸−10

5.97𝐸+00

APSO

9.60𝐸−66

1.83𝐸+01

1.09𝐸−14

1.20𝐸−02

4.77𝐸−02

6.27𝐸+00

2.27𝐸+00

2.13𝐸+03

1.22𝐸+00

1.38𝐸−02

8.40𝐸+00

7.09𝐸+01

NSPSO

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟒.𝟎𝟖𝐄+𝟎𝟎

5.89𝐸−16

𝟎.𝟎𝟎𝐄+𝟎𝟎

6.72𝐸−13

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟎.𝟎𝟎𝐄+𝟎𝟎

1.07𝐸+03

9.55𝐸−13

𝟎.𝟎𝟎𝐄+𝟎𝟎

1.54𝐸−13

𝟎.𝟎𝟎𝐄+𝟎𝟎

NSBPSO

𝟎.𝟎𝟎𝐄+𝟎𝟎

2.01𝐸+01

5.89𝐸−16

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟎.𝟎𝟎𝐄+𝟎𝟎

1.01𝐸+03

𝟓.𝟖𝟗𝐄−𝟏𝟔

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟎.𝟎𝟎𝐄+𝟎𝟎

𝟎.𝟎𝟎𝐄+𝟎𝟎