Hierarchical Swarm Model: A New Approach to Optimization

Table 3

Performance of all algorithms on benchmark functions 𝑓₁-𝑓₅. 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	0	0	6.24𝑒−305	0	2.42𝑒−114	1.73𝑒−029	3.71𝑒−183	2.47𝑒−169	0	5.52𝑒−016
f1	Std	𝟎	𝟎	𝟎	𝟎	3.39𝑒−114	2.29𝑒−029	𝟎	𝟎	𝟎	8.47𝑒−017
	Rank	𝟏	𝟏	4	𝟏	7	8	6	5	𝟏	10
	Mean	1.32𝑒−001	1.04𝑒−014	2.55𝑒−016	3.71𝑒−026	6.61𝑒+000	2.25𝑒+001	2.09𝑒+000	2.79𝑒−001	𝟕.𝟗𝟏𝐞−𝟎𝟐𝟗	8.80𝑒−002
f2	Std	7.27𝑒−001	9.71𝑒−015	1.70𝑒−016	1.09𝑒−025	4.02𝑒−001	1.27𝑒+000	7.69𝑒−001	1.02𝑒+000	𝟏.𝟕𝟕𝐞−𝟎𝟐𝟗	7.98𝑒−002
	Rank	6	4	3	2	9	10	8	7	𝟏	5
	Mean	1.04𝑒−090	2.19𝑒−047	1.42𝑒−051	2.50𝑒−092	3.51𝑒−018	1.38𝑒+000	6.12𝑒−013	4.25𝑒−014	𝟑.𝟗𝟓𝐞−𝟐𝟑𝟓	1.16𝑒+001
f3	Std	5.01𝑒−090	6.82𝑒−047	4.28𝑒−051	1.02𝑒−091	7.88𝑒−018	1.00𝑒+000	6.06𝑒−013	2.32𝑒−013	𝟎	4.57𝑒+000
	Rank	3	5	4	2	6	10	8	7	𝟏	9
	Mean	𝟎	𝟎	𝟎	8.23𝑒−320	4.54𝑒−185	5.03𝑒−065	𝟎	8.64𝑒−280	9.48𝑒−006	7.75𝑒−006
f4	Std	𝟎	𝟎	𝟎	𝟎	𝟎	2.38𝑒−064	𝟎	𝟎	1.27𝑒−005	8.50𝑒−006
	Rank	𝟏	𝟏	𝟏	5	7	8	𝟏	6	10	9
	Mean	𝟎	𝟎	1.38𝑒−002	1.14𝑒−001	4.84𝑒−002	1.38𝑒−002	𝟎	3.50𝑒−003	9.28𝑒−032	5.68𝑒−016
f5	Std	𝟎	𝟎	3.58𝑒−002	2.80𝑒−001	8.04𝑒−002	4.50𝑒−002	𝟎	1.89𝑒−002	6.57𝑒−033	8.19𝑒−017
	Rank	𝟏	𝟏	7	10	9	8	𝟏	6	4	5
Aver. Rank		𝟐𝟒	𝟐.𝟒	3.8	4	9.5	8.8	4.8	6.2	3.4	7.6
Final Rank		𝟏	𝟏	4	5	10	9	6	7	3	8