Complexity Reduction in the Use of Evolutionary Algorithms to Function Optimization: A Variable Reduction Strategy

Table 2

Optimization results obtained for the frequency-modulated synthesizer optimization problem; the results obtained by EAs with VRS are shown in boldface.

Algorithm	Best	Worst	Mean	Std
PSO-w	0.0	1.258023𝑒+001	3.752319𝑒+000	5.853543𝑒+000
PSO-w-VRS	0.0	𝟏.𝟐𝟓𝟒𝟎𝟏𝟒𝐞+𝟎𝟎𝟏	𝟑.𝟑𝟕𝟓𝟔𝟐𝟎𝐞+𝟎𝟎𝟎	𝟓.𝟖𝟗𝟑𝟓𝟒𝟑𝐞+𝟎𝟎𝟎
PSO-cf	2.673488𝑒−006	2.180154𝑒+001	1.200588𝑒+001	5.144827𝑒+000
PSO-cf-VRS	𝟒.𝟐𝟕𝟓𝟏𝟑𝟔𝐞−𝟎𝟎𝟕	𝟏.𝟐𝟏𝟕𝟗𝟏𝟕𝐞+𝟎𝟎𝟏	𝟖.𝟒𝟔𝟔𝟒𝟒𝟑𝐞+𝟎𝟎𝟎	𝟒.𝟖𝟒𝟖𝟒𝟓𝟎𝐞+𝟎𝟎𝟎
UPSO	5.839747𝑒−028	1.473172𝑒+001	6.608215𝑒+000	4.636487𝑒+000
UPSO-VRS	0.0	𝟏.𝟏𝟐𝟎𝟕𝟏𝟗𝐞+𝟎𝟎𝟏	𝟔.𝟒𝟐𝟓𝟎𝟐𝟕𝐞+𝟎𝟎𝟎	𝟒.𝟏𝟖𝟓𝟏𝟕𝟒𝐞+𝟎𝟎𝟎
FDR	0.0	2.016705𝑒+001	1.191916𝑒+001	6.193037𝑒+000
FDR-VRS	0.0	𝟏.𝟐𝟓𝟒𝟎𝟔𝟖𝐞+𝟎𝟎𝟏	𝟏.𝟎𝟓𝟓𝟕𝟏𝟏𝐞+𝟎𝟎𝟏	𝟑.𝟔𝟐𝟔𝟓𝟏𝟖𝐞+𝟎𝟎𝟎
FIPS	3.321497𝑒−003	8.500601𝑒+000	2.306348𝑒+000	2.513825𝑒+000
FIPS-VRS	𝟗.𝟑𝟖𝟖𝟎𝟗𝟖𝐞−𝟎𝟏𝟎	𝟐.𝟕𝟖𝟕𝟕𝟔𝟔𝐞+𝟎𝟎𝟎	𝟏.𝟏𝟐𝟕𝟕𝟗𝟒𝐞+𝟎𝟎𝟎	𝟏.𝟑𝟓𝟗𝟑𝟏𝟓𝐞+𝟎𝟎𝟎
CPSO-H	1.179023𝑒+001	2.553845𝑒+001	1.910668𝑒+001	4.381173𝑒+000
CPSO-H-VRS	𝟕.𝟕𝟖𝟑𝟗𝟖𝟏𝐞−𝟎𝟎𝟏	𝟏.𝟔𝟖𝟑𝟓𝟕𝟏𝐞+𝟎𝟎𝟏	𝟏.𝟐𝟕𝟒𝟓𝟏𝟖𝐞+𝟎𝟎𝟏	𝟓.𝟎𝟓𝟖𝟔𝟖𝟕𝐞+𝟎𝟎𝟎
CLPSO	1.354023𝑒−004	1.138270𝑒+001	1.666438𝑒+000	3.567321𝑒+000
CLPSO-VRS	𝟐.𝟑𝟎𝟗𝟑𝟐𝟕𝐞−𝟎𝟎𝟓	𝟔.𝟓𝟒𝟏𝟑𝟎𝟓𝐞+𝟎𝟎𝟎	𝟑.𝟕𝟑𝟒𝟗𝟔𝟐𝐞−𝟎𝟎𝟏	𝟏.𝟒𝟓𝟔𝟑𝟖𝟖𝐞+𝟎𝟎𝟎