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

Table 5

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

Test functions	GD	NSGA-II	SPEA-II	MOPSO	NSGA-III	IMOPSO
ZDT1	Average	7.71E − 3	2.09E − 2	1.01E − 2	2.84E − 3	1.08E − 4
	Std. dev.	7.28E − 4	2.31E − 2	9.59E − 4	5.95E − 4	1.37E − 5
ZDT2	Average	7.69E − 3	2.32E − 2	2.53E − 2	9.60E − 4	4.15E − 3
	Std. dev.	8.98E − 3	1.92E − 3	4.81E − 3	4.83E − 4	6.47E − 3
ZDT3	Average	6.74E − 4	1.15E − 3	1.25E − 1	1.69E − 3	6.91E − 5
	Std. dev.	1.59E − 4	5.85E − 4	2.91E − 2	4.51E − 4	3.25E − 5
ZDT4	Average	2.34E − 2	1.22E + 0	6.41E − 3	6.19E − 3	1.24E − 3
	Std. dev.	2.60E − 2	1.78E + 0	7.63E − 3	1.73E − 3	1.07E − 3
ZDT6	Average	8.69E − 3	5.37E − 3	2.76E − 1	6.53E − 2	2.29E − 3
	Std. dev.	3.69E − 3	5.43E − 3	3.43E − 1	3.29E − 2	1.79E − 3
DTLZ1	Average	4.19E − 2	1.94E − 1	7.11E + 0	4.14E − 2	2.15E − 2
	Std. dev.	5.18E − 2	2.78E − 1	1.92E + 0	3.36E − 2	2.09E − 2
DTLZ2	Average	1.31E − 3	1.47E − 3	8.90E − 3	6.08E − 5	1.68E − 3
	Std. dev.	6.54E − 3	2.00E − 4	2.70E − 3	4.65E − 5	3.73E − 4
DTLZ3	Average	1.48E + 0	1.14E + 1	2.91E + 1	2.89E + 1	1.09E + 0
	Std. dev.	3.74E + 0	8.16E + 0	1.03E + 1	5.39E + 1	3.87E − 1
DTLZ4	Average	1.98E − 3	2.09E − 3	3.96E − 2	5.76E − 4	1.56E − 3
	Std. dev.	2.30E − 4	1.36E − 4	2.59E − 2	1.39E − 4	2.13E − 4
DTLZ5	Average	2.70E − 4	3.19E − 4	1.58E − 3	3.25E − 4	1.88E − 4
	Std. dev.	7.01E − 5	8.19E − 5	1.06E − 3	8.32E − 5	6.59E − 5
DTLZ6	Average	1.31E − 5	5.94E − 3	7.11E − 2	4.26E − 1	5.19E − 6
	Std. dev.	4.53E − 5	9.37E − 2	4.28E − 3	1.72E − 2	2.97E − 7
DTLZ7	Average	7.06E − 3	6.18E − 3	5.97E − 1	6.85E − 3	3.13E − 3
	Std. dev.	1.56E − 3	1.60E − 3	4.03E − 1	2.24E − 3	1.06E − 3