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

Table 1

Optimization results obtained for the test functions; the best results are shown in boldface.

Algorithm	Mean	Std	FEs	Mean	Std	FEs
	Rosenbrock function			Variably dimensioned function
PSO-w	2.182𝑒+000	2.642𝑒−002	30 000	1.576𝑒+003	4.610𝑒+002	200 000
PSO-cf	3.833𝑒−001	0.250𝑒+000	30 000	5.618𝑒+000	1.385𝑒+001	200 000
UPSO	1.055𝑒+000	1.542𝑒+000	30 000	1.164𝑒+003	4.763𝑒+002	200 000
FDR	6.480𝑒−001	6.846𝑒−001	30 000	3.188𝑒−001	5.820𝑒−001	200 000
FIPS	1.186𝑒+000	1.080𝑒−001	30 000	4.479𝑒+003	1.317𝑒+003	200 000
CPSO-H	1.044𝑒+000	1.265𝑒+000	30 000	1.365𝑒+004	3.277𝑒+003	200 000
CLPSO	1.262𝑒+000	9.658𝑒−001	30 000	2.889𝑒+003	6.235𝑒+002	200 000
PSO-VRS	0.0	0.0	11 565	0.0	0.0	12 684
Algorithm	Wood function			Ackley function
PSO-w	3.347𝑒−006	3.383𝑒−006	200 000	3.942𝑒−014	1.123𝑒+000	200 000
PSO-cf	9.784𝑒−006	2.225𝑒−007	200 000	1.123𝑒+000	8.655𝑒−001	200 000
UPSO	1.459𝑒−009	5.144𝑒−009	200 000	1.225𝑒−015	3.162𝑒−015	200 000
FDR	1.576𝑒−009	1.589𝑒−009	200 000	2.844𝑒−014	4.107𝑒−015	200 000
FIPS	5.868𝑒−005	7.834𝑒−005	200 000	4.812𝑒−007	9.172𝑒−008	200 000
CPSO-H	5.861𝑒−001	2.616𝑒−001	200 000	4.931𝑒−014	1.104𝑒−014	200 000
CLPSO	1.570𝑒−002	3.330𝑒−002	200 000	0.0	0.0	180 864
PSO-VRS	0.0	0.0	13 078	0.0	0.0	11 254