Global Particle Swarm Optimization for High Dimension Numerical Functions Analysis

Table 5

Best, worst, mean, and standard deviation values obtained by PSO, IPSO, EPSO, and GPSO through 50 independent runs on functions from 𝑓₁₀ to 𝑓₁₂.

Function	Dim.	Min.		Best	Worst	Mean	SD
𝑓10	20		PSO	−70.2000	−52.8000	−61.2000	3.5700
			IPSO	−68.3000	−57.7000	−62.0000	2.5100
			EPSO	−60.6000	−40.3000	−51.7000	4.8822
			GPSO	−78.3000	−75.1000	−77.9000	0.6716
	30		PSO	−63.2295	−49.5756	−56.2019	3.0588
			IPSO	−64.0370	−51.9089	−57.1815	2.7452
			EPSO	−56.0959	−39.0376	−47.4010	3.6965
		−78.3324	GPSO	−78.3323	−78.3323	−78.3323	0.0000
	50		PSO	−60.4579	−44.9971	−51.2624	3.1199
			IPSO	−56.2791	−46.6235	−51.8837	2.3331
			EPSO	−50.3900	−35.8658	−43.2473	3.2610
			GPSO	−78.3323	−78.3323	−78.3323	0.0000
	100		PSO	−51.1000	−40.1000	−45.0000	2.5976
			IPSO	−53.2000	−43.0000	−47.4000	2.0405
			EPSO	−38.7000	−31.9000	−35.4000	1.7196
			GPSO	−78.3000	−76.1000	−78.0000	0.3840
𝑓11	20		PSO	3.06𝐸+00	1.29𝐸+01	7.89𝐸+00	2.31𝐸+00
			IPSO	1.50𝐸+00	8.32𝐸+00	3.51𝐸+00	1.33𝐸+00
			EPSO	9.03𝐸+00	2.56𝐸+01	1.45𝐸+01	3.76𝐸+00
			GPSO	1.27𝐸−05	1.46𝐸−04	5.62𝐸−05	3.10𝐸−05
	30		PSO	6.60𝐸+00	2.74𝐸+01	1.67𝐸+01	3.87𝐸+00
			IPSO	4.28𝐸+00	1.44𝐸+01	9.31𝐸+00	2.13𝐸+00
			EPSO	1.38𝐸+01	4.03𝐸+01	2.58𝐸+01	6.66𝐸+00
		0	GPSO	1.80𝐸−05	1.64𝐸−04	7.93𝐸−05	4.18𝐸−05
	50		PSO	2.32𝐸+01	5.53𝐸+01	3.60𝐸+01	7.14𝐸+00
			IPSO	1.58𝐸+01	3.40𝐸+01	2.31𝐸+01	3.56𝐸+00
			EPSO	3.10𝐸+01	7.10𝐸+01	5.45𝐸+01	7.73𝐸+00
			GPSO	2.48𝐸−05	3.85𝐸−04	1.26𝐸−04	8.52𝐸−05
	100		PSO	5.91𝐸+01	1.32𝐸+02	8.94𝐸+01	1.35𝐸+01
			IPSO	4.66𝐸+01	7.38𝐸+01	5.98𝐸+01	5.72𝐸+00
			EPSO	8.55𝐸+01	1.54𝐸+02	1.17𝐸+02	1.66𝐸+01
			GPSO	3.97𝐸−05	7.27𝐸−04	2.68𝐸−04	1.58𝐸−04
𝑓12	20		PSO	1.23𝐸+01	1.03𝐸+02	4.55𝐸+01	2.02𝐸+01
			IPSO	4.72𝐸+00	4.97𝐸+01	2.22𝐸+01	9.20𝐸+00
			EPSO	3.10𝐸+01	2.09𝐸+02	1.17𝐸+02	3.92𝐸+01
			GPSO	1.41𝐸−07	2.29𝐸−05	5.91𝐸−06	6.27𝐸−06
	30		PSO	5.68𝐸+01	2.56𝐸+02	1.15𝐸+02	4.38𝐸+01
			IPSO	1.72𝐸+01	1.05𝐸+02	5.24𝐸+01	1.76𝐸+01
			EPSO	9.89𝐸+01	3.54𝐸+02	2.11𝐸+02	6.05𝐸+01
		0	GPSO	8.08𝐸−08	6.49𝐸−05	1.14𝐸−05	1.34𝐸−05
	50		PSO	1.14𝐸+02	3.91𝐸+02	2.14𝐸+02	5.72𝐸+01
			IPSO	7.01𝐸+01	1.98𝐸+02	1.30𝐸+02	2.79𝐸+01
			EPSO	1.89𝐸+02	6.68𝐸+02	4.38𝐸+02	1.23𝐸+02
			GPSO	5.00𝐸−07	1.50𝐸−04	2.25𝐸−05	2.59𝐸−05
	100		PSO	3.55𝐸+02	9.73𝐸+02	5.96𝐸+02	1.40𝐸+02
			IPSO	2.47𝐸+02	4.99𝐸+02	3.57𝐸+02	5.63𝐸+01
			EPSO	5.21𝐸+02	1.38𝐸+03	1.03𝐸+03	1.70𝐸+02
			GPSO	4.74𝐸−07	4.71𝐸−04	4.28𝐸−05	7.74𝐸−05