Particle Swarm Optimization Algorithm with Multiple Phases for Solving Continuous Optimization Problems

Table 2

Experimental results for functions with 50 dimensions.

Algorithm		Best	Mean	St.D.	Best	Mean	St.D.
		parabolic			Schwefel’s P2.22
SPSO-BK	Star	−450	−450	4.52E-13	−330	−329.9999	1.35E-11
	Ring	−449.9999	−449.9999	2.11E-12	−329.9999	−329.9999	4.37E-12
SPSO-C	Star	−449.9999	−449.9999	4.12E-09	−329.9999	−329.9999	3.08E-05
	Ring	−449.9999	−449.9999	3.13E-12	−329.9999	−329.9999	6.01E-12
CPSO	Star	−450	−450	5.90E-14	−330	−329.8	1.4
	Ring	−373.3774	−191.0975	98.981	−329.8322	−325.9999	2.151
PSOFP		−450	−450	1.47E-12	−329.9999	−329.9999	6.25E-09
PSODP		−450	−450	1.91E-12	−329.9999	−329.9999	1.45E-06
		Schwefel’s P1.2			step
SPSO-BK	Star	450.0000	550.0000	699.9999	180	188.36	13.936
	Ring	455.3668	495.6626	38.833	266	360.46	50.708
SPSO-C	Star	450.0000	450.3961	2.748	207	343.66	106.891
	Ring	450.0958	451.3167	2.5006	373	714.3	167.178
CPSO	Star	476.3968	602.0931	697.433	180	180	0
	Ring	3121.6019	4966.1359	769.950	395	534.64	70.468
PSOFP		450.0476	454.3896	29.0223	180	180.4	2.107
PSODP		450.0013	460.0571	34.158	180	187.54	26.872
		quartic noise			Rosenbrock
SPSO-BK	Star	120.0022	120.0044	0.001	−449.9976	−418.4438	24.245
	Ring	120.0281	120.0630	0.023	−444.3137	−415.0037	9.573
SPSO-C	Star	120.0408	120.1508	0.070	−449.9999	−448.3351	2.378
	Ring	120.0467	120.2094	0.085	−443.4564	−411.7220	17.957
CPSO	Star	120.0037	120.0090	0.002	−421.5111	−389.7360	27.273
	Ring	120.0194	120.0321	0.006	−218.8776	193.7953	156.862
PSOFP		120.0026	120.0061	0.0024	−439.0752	−395.1315	31.0671
PSODP		120.0029	120.0086	0.0076	−444.2963	−405.6357	25.7581