Hierarchical Swarm Model: A New Approach to Optimization

Table 5

Performance of all algorithms on benchmark functions 𝑓₁₁-𝑓₁₇. In bold are the best results.

Func.		PS^2O-S	PS^2O-R	PS^2O-SR	PS^2O-RS	PSO	GA
f11	Mean	𝟎	𝟎	1.67𝑒−002	𝟎	2.14𝑒+000	1.26𝑒−001
	Std	𝟎	𝟎	5.31𝑒−002	𝟎	2.60𝑒−001	1.41𝑒−001
	Iter.	𝟏𝟒	24	335	28	∞	∞
	Rank	𝟏	2	4	3	6	5
f12	Mean	𝟎	𝟎	3.33𝑒−002	𝟎	3.19𝑒+000	2.64𝑒−001
	Std	𝟎	𝟎	1.18𝑒−001	𝟎	3.81𝑒−001	1.06𝑒−001
	Iter.	310	𝟔𝟗	493	328	∞	∞
	Rank	2	𝟏	4	3	6	5
f13	Mean	𝟎	𝟎	𝟎	𝟎	3.96𝑒+000	𝟎
	Std	𝟎	𝟎	𝟎	𝟎	1.33𝑒+000	𝟎
	Iter.	134	𝟖𝟐	426	275	∞	335
	Rank	2	𝟏	5	3	6	4
f14	Mean	4.00𝑒−003	𝟎	6.70𝑒−003	𝟎	2.94𝑒−001	2.38𝑒−001
	Std	1.98𝑒−002	𝟎	2.54𝑒−002	𝟎	1.33𝑒−002	8.05𝑒−002
	Iter.	871	𝟑𝟔𝟕	538	398	∞	∞
	Rank	4	𝟏	3	2	6	5
f15	Mean	𝟎	𝟎	𝟎	𝟎	𝟎	1.36𝑒−001
	Std	𝟎	𝟎	𝟎	𝟎	𝟎	1.30𝑒−001
	Iter.	𝟏𝟕	89	147	107	356	∞
	Rank	𝟏	2	4	3	5	6
f16	Mean	𝟎	𝟎	𝟎	𝟎	2.00𝑒−003	1.80𝑒−001
	Std	𝟎	𝟎	𝟎	𝟎	1.41𝑒−002	2.44𝑒−001
	Iter.	203	272	187	𝟏𝟓𝟏	∞	∞
	Rank	3	4	2	𝟏	5	6
	Mean	𝟎	𝟎	𝟎	𝟎	𝟎	7.44𝑒−002
f17	Std	𝟎	𝟎	𝟎	𝟎	𝟎	1.83𝑒−002
	Iter.	𝟑𝟗	51	𝟑𝟗	55	61	∞
	Rank	𝟏	3	𝟏	4	5	6
	Aver. Rank	𝟐	𝟐	3.29	2.71	5.57	5.14
	Final Rank	𝟏	𝟏	4	3	6	5