Global Particle Swarm Optimization for High Dimension Numerical Functions Analysis

Table 6

The average (mean) and standard deviation values of GPSO with various acceleration coefficients for all functions.

Function	Performance of GPSO for different 𝑐1,𝑐2, and 𝑐3 values in 50 trials for Dim. = 50 cases
	𝑐1=𝑐2=𝑐3=0.2		𝑐1=𝑐2=𝑐3=0.5		𝑐1=𝑐2=𝑐3=1.0		𝑐1=𝑐2=𝑐3=1.5		𝑐1=𝑐2=𝑐3=2.0
	Average	Std Dev.	Average	Std Dev.	Average	Std Dev.	Average	Std Dev.	Average	Std Dev.
𝑓1	1.02𝐸−06	1.40𝐸−06	5.45𝐸−06	4.68𝐸−06	7.37𝐸−04	8.00𝐸−04	4.69𝐸−01	5.46𝐸−01	3.42𝐸+01	3.24𝐸+01
𝑓2	2.32𝐸−07	2.41𝐸−07	1.48𝐸−06	1.40𝐸−06	1.60𝐸−04	2.16𝐸−04	2.27𝐸−01	3.10𝐸−01	9.45𝐸+00	7.47𝐸+00
𝑓3	7.75𝐸−11	1.44𝐸−10	3.33𝐸−10	4.83𝐸−10	3.79𝐸−08	5.18𝐸−08	1.12𝐸−05	1.35𝐸−05	1.13𝐸−03	1.19𝐸−03
𝑓4	9.39𝐸−07	8.96𝐸−07	7.55𝐸−06	9.15𝐸−06	5.83𝐸−04	6.42𝐸−04	5.56𝐸−01	6.05𝐸−01	3.23𝐸+01	3.16𝐸+01
𝑓5	1.84𝐸−04	9.71𝐸−05	4.25𝐸−04	2.91𝐸−04	3.57𝐸−03	1.97𝐸−03	2.22𝐸−01	1.86𝐸−01	2.39𝐸+00	7.81𝐸−01
𝑓6	8.81𝐸−06	1.30𝐸−05	3.97𝐸−05	3.53𝐸−05	2.97𝐸−03	2.63𝐸−03	3.30𝐸−01	4.93𝐸−01	2.80𝐸+01	2.76𝐸+01
𝑓7	1.79𝐸−06	3.42𝐸−06	4.82𝐸−05	6.43𝐸−05	3.63𝐸−03	4.23𝐸−03	1.30𝐸−01	3.87𝐸−01	1.26𝐸+01	1.46𝐸+01
𝑓8	1.05𝐸−05	2.04𝐸−05	1.85𝐸−04	2.08𝐸−04	2.92𝐸−03	3.61𝐸−03	5.42𝐸−02	7.07𝐸−02	6.27𝐸+00	6.51𝐸+00
𝑓9	−7.83𝐸+1	2.85𝐸−09	−7.83𝐸+1	2.21𝐸−08	−7.83𝐸+1	7.68𝐸−07	−7.83𝐸+1	8.78𝐸−04	−7.77𝐸+1	4.01𝐸+00
𝑓10	8.02𝐸−05	4.92𝐸−05	1.26𝐸−04	8.52𝐸−05	9.97𝐸−04	7.55𝐸−04	1.68𝐸−02	9.63𝐸−03	3.15𝐸−01	3.05𝐸−01
𝑓11	2.01𝐸−06	2.66𝐸−06	2.25𝐸−05	2.59𝐸−05	1.43𝐸−03	1.75𝐸−03	9.45𝐸−01	9.93𝐸−01	1.10𝐸+01	5.69𝐸+00
𝑓12	8.81𝐸−06	1.30𝐸−05	3.97𝐸−05	3.53𝐸−05	2.97𝐸−03	2.63𝐸−03	3.30𝐸−01	4.93𝐸−01	2.80𝐸+01	2.76𝐸+01