Hierarchical Swarm Model: A New Approach to Optimization

Table 4

Performance of all algorithms on benchmark functions 𝑓₆-𝑓₁₀. In bold are the best results.

Func.		PS^2O-S	PS^2O-R	PS^2O-SR	PS^2O-RS	PSO	FIPS	UPSO	FDR-PSO	CMA-ES	ABC
	Mean	7.11𝑒−015	4.74𝑒−015	4.97𝑒−015	8.32𝑒−002	6.16𝑒−015	2.04𝑒−014	𝟑.𝟓𝟓𝐞−𝟎𝟏𝟓	2.74𝑒−014	1.96𝑒+001	4.79𝑒−014
f6	Std	𝟎	1.70𝑒−015	1.77𝑒−015	3.17𝑒−002	1.80𝑒−015	1.08𝑒−014	3.16𝑒−015	1.03𝑒−014	4.30𝑒−001	6.09𝑒−015
	Rank	𝟏	3	4	9	5	6	2	7	10	8
	Mean	4.47𝑒+001	3.25𝑒+001	3.61𝑒+001	4.61𝑒+001	2.78𝑒+001	4.13𝑒+001	4.96𝑒+001	2.60𝑒+001	7.56𝑒+000	𝟏.𝟔𝟒𝐞−𝟎𝟏𝟑
f7	Std	1.20𝑒+001	8.41𝑒+000	8.96𝑒+000	1.11𝑒+001	5.46𝑒+000	2.34𝑒+001	9.80𝑒+000	8.32𝑒+000	2.15𝑒+000	𝟔.𝟐𝟓𝐞−𝟎𝟏𝟒
	Rank	9	5	6	8	4	7	10	3	2	𝟏
	Mean	8.37𝑒−003	𝟎	𝟎	9.26𝑒−003	1.83𝑒−002	1.56𝑒−003	3.47𝑒−003	1.79𝑒−002	𝟎	1.03𝑒−015
f8	Std	1.09𝑒−002	𝟎	𝟎	1.07𝑒−002	2.66𝑒−002	3.78𝑒−003	4.78𝑒−003	1.82𝑒−002	𝟎	1.17𝑒−015
	Rank	7	𝟏	𝟏	8	10	5	6	9	𝟏	4
	Mean	1.17𝑒+000	𝟎	𝟎	1.22𝑒+000	1.35𝑒+000	2.01𝑒−002	4.42𝑒+000	1.58𝑒−001	2.15𝑒+000	𝟎
f9	Std	7.68𝑒−001	𝟎	𝟎	8.64𝑒−001	1.16𝑒+000	5.58𝑒−002	2.60𝑒+000	4.56𝑒−001	2.98𝑒+000	𝟎
	Rank	6	𝟏	𝟏	7	8	4	10	5	9	𝟏
	Mean	𝟎	𝟎	𝟎	4.00𝑒+001	5.00𝑒+001	3.37𝑒+001	8.00𝑒+001	1.00𝑒+002	1.30𝑒+002	3.83𝑒−002
f10	Std	𝟎	𝟎	𝟎	8.94𝑒+000	1.82𝑒+002	2.58𝑒+001	4.42𝑒+001	4.42𝑒+001	1.63𝑒+002	1.21𝑒−001
	Rank	𝟏	𝟏	𝟏	6	7	5	8	9	10	4
Aver. Rank		4.8	𝟐.𝟐	2.6	7.6	6.8	5.4	7.2	6.6	6.4	3.6
Final Rank		4	𝟏	2	10	8	5	9	7	6	3