A Multiobjective Particle Swarm Optimization Algorithm Based on Competition Mechanism and Gaussian Variation

Table 6

Statistical results of SP obtained by different methods for different test functions.

Test functions	SP	NSGA-II	SPEA-II	MOPSO	NSGA-III	IMOPSO
ZDT1	Average	7.33E − 3	8.97E − 3	1.28E − 2	1.08E − 2	6.47E − 3
	Std. dev.	6.77E − 4	1.91E − 3	2.18E − 3	1.65E − 3	6.34E − 4
ZDT2	Average	7.85E − 3	8.99E − 3	7.88E − 3	1.19E − 2	7.79E − 3
	Std. dev.	2.34E − 3	4.61E − 3	5.74E − 3	5.76E − 3	1.75E − 3
ZDT3	Average	8.16E − 3	1.05E − 2	1.37E − 2	1.06E − 2	7.101E − 3
	Std. dev.	9.32E − 4	2.06E − 3	5.40E − 3	1.46E − 3	9.28E − 4
ZDT4	Average	2.76E − 2	1.36E − 1	3.70E − 2	6.09E − 3	1.81E − 2
	Std. dev.	2.79E − 2	3.62E − 1	3.93E − 2	2.83E − 2	5.27E − 2
ZDT6	Average	1.73E − 2	1.61E − 2	8.82E − 2	4.23E − 2	1.19E − 2
	Std. dev.	3.55E − 2	3.80E − 2	6.13E − 2	2.08E − 2	4.01E − 3
DTLZ1	Average	5.81E − 2	1.44E + 0	5.51E + 0	6.13E − 2	3.93E − 1
	Std. dev.	4.41E − 2	3.27E + 0	1.45E + 0	3.27E − 2	4.01E − 1
DTLZ2	Average	6.17E − 2	5.20E − 2	6.15E − 2	5.78E − 2	5.95E − 2
	Std. dev.	5.23E − 3	5.61E − 3	9.19E − 3	1.79E − 3	4.90E − 3
DTLZ3	Average	7.71E + 0	2.56E + 0	6.63E + 1	1.70E + 1	1.32E + 0
	Std. dev.	3.18E + 0	5.06E + 0	2.89E + 1	5.32E − 1	2.20E + 0
DTLZ4	Average	5.44E − 2	4.426E − 2	4.97E − 2	5.17E − 2	6.12E − 2
	Std. dev.	1.36E − 2	4.76E − 3	3.12E − 2	2.15E − 2	4.87E − 3
DTLZ5	Average	1.04E − 2	1.32E − 2	1.38E − 2	1.52E − 2	9.79E − 3
	Std. dev.	1.18E − 3	2.12E − 3	1.06E − 3	2.91E − 3	8.04E − 4
DTLZ6	Average	1.13E − 2	2.793E − 1	1.38E − 2	2.19E − 2	1.22E − 2
	Std. dev.	8.87E − 4	5.09E − 2	1.01E − 1	2.50E − 2	1.25E − 3
DTLZ7	Average	7.03E − 2	4.55E − 2	5.97E − 1	6.48E − 2	3.56E − 2
	Std. dev.	6.89E − 3	1.63E − 2	2.65E − 2	8.90E − 3	2.33E − 3