Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches

Table 9

Comparison of the results of the proposed RGA-PSO and AIA-PSO approaches and those of the hybrid algorithms for 11 TPs.

TP number	Function; name	𝑀𝐸s
		NM-PSO [9]	PSACO [10]	GA-PSO [9]	DE-PSO [12]	AM-PSO1 [12]	AM-PSO2 [12]	CHA [10]	CTSS [10]	AIA-PSO; (this work)	RGA-PSO; (this work)
2	GP	0.00003	0.00000000	0.00012	3.67𝐸−5	3.81𝐸−5	9.89𝐸−6	0.0010	0.001	0.00000000	0.00000000
3	ES	0.00004	0.00000000	0.00003	1.67𝐸−5	4.10𝐸−5	3.71𝐸−5	0.0010	0.005	0.00000000	0.00000000
4	B2	0.00003	5.5511𝐸−17	0.00001	1.11𝐸−5	1.17𝐸−6	2.64𝐸−5	0.0000002	0.000005	0.00000000	0.00000000
5	DJ	0.00003	7.6900𝐸−29	0.00004	1.67𝐸−5	4.23𝐸−5	3.34𝐸−5	0.0002	0.0002	𝟐.𝟓𝟒𝟒𝐄−𝟐𝟏𝟓	𝟓.𝟓𝟑𝟑𝟏𝐄−𝟐𝟐𝟔
7	RC	0.00003	2.6185𝐸−13	0.00009	2.29𝐸−6	1.52𝐸−5	1.49𝐸−5	0.0001	0.005	0.00000000	0.00000000
9	RS2	0.00003	1.7152𝐸−10	0.00064	2.46𝐸−5	2.16𝐸−5	3.33𝐸−5	0.0040	0.0040	𝟐.𝟑𝟒𝟏𝐄−𝟐𝟕	𝟖.𝟕𝟎𝟗𝐄−𝟐𝟖
10	RS5	0.0056	1.8538𝐸−04	0.00013	7.74𝐸−5	9.73𝐸−5	9.93𝐸−5	—	—	𝟕.𝟐𝟗𝟏𝐄−𝟎𝟔	𝟗.𝟒𝟓𝟐𝐄−𝟎𝟔
11	SH	0.00002	1.09239𝐸−09	0.00007	3.03𝐸−6	1.72𝐸−5	2.54𝐸−7	0.0050	0.001	0.00000000	0.00000000
12	ZA2	0.00003	5.7061𝐸−27	0.00005	1.12𝐸−5	2.54𝐸−5	2.61𝑍𝐸−6	3𝐸−6	3𝐸−7	0.00000000	0.00000000
13	ZA5	0.00026	3.6352𝐸−17	0.00000	3.49𝐸−5	3.44𝐸−5	5.07𝐸−5	—	—	𝟕.𝟐𝟓𝟗𝐄−𝟏𝟖𝟒	𝟐.𝟔𝟔𝟎𝐄−𝟏𝟏𝟕
14	ZA10	—	2𝐸−08	0.00000	6.91𝐸−5	7.41𝐸−5	9.11𝐸−5	1𝐸−6	—	𝟑.𝟐𝟖𝟕𝐄−𝟒𝟐	𝟒.𝟑𝟕𝟓𝟔𝐄−𝟐𝟔

(“—” denotes unavailable information).