Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches

Table 4

Numerical results obtained from the proposed AIA-PSO algorithm for solving 14 UGO problems.

TP number	Function name	Global minimum	Required accuracy	Success rate (%)	𝑓(𝐱^∗AIA-PSO)	𝑓(𝐱^meanAIA-PSO)	𝑓(𝐱^worstAIA-PSO)	ME	MCCT (sec)
1	SHCB	−1.0316	1𝐸−4	100	−1.0316	−1.0316	−1.0316	0.00000000	39.69
2	GP	3	1𝐸−3	100	3	3	3	0.00000000	37.80
3	ES	−1	1𝐸−3	100	−1	−1	−1	0.00000000	42.08
4	B2	0	1𝐸−2	100	0.00000000	0.00000000	0.00000000	0.00000000	40.43
5	DJ	0	1𝐸−4	100	0.00000000	2.544𝐸−215	2.544𝐸−213	2.544𝐸−215	39.43
6	Booth	0	1𝐸−4	100	0.00000000	0.00000000	0.00000000	0.00000000	37.48
7	RC	5/4𝜋	1𝐸−3	100	0.39788735	0.39788735	0.39788735	0.00000000	40.53
8	RA	−2	1𝐸−4	100	−2	−2	−2	0.00000000	39.17
9	RS2	0	1𝐸−3	100	0.00000000	2.341𝐸−27	2.129𝐸−25	2.341𝐸−27	37.49
10	RS5	0	1𝐸−3	100	4.342𝐸−10	7.291𝐸−06	9.313𝐸−05	7.291𝐸−06	304.23
11	SH	−186.7309	1𝐸−2	100	−186.7309	−186.7309	−186.7309	0.00000000	54.70
12	ZA2	0	1𝐸−4	100	0.00000000	0.00000000	0.00000000	0.00000000	40.31
13	ZA5	0	1𝐸−4	100	0.00000000	7.2591𝐸−184	7.259𝐸−182	7.259𝐸−184	144.38
14	ZA10	0	1𝐸−3	100	1.472𝐸−120	3.287𝐸−42	2.856𝐸−40	3.287𝐸−42	192.06

𝑓(𝐱^∗_AIA-PSO): the objective value obtained using the best AIA-PSO solution.
𝑓(𝐱^mean_AIA-PSO): mean objective value obtained using the AIA-PSO solutions.
𝑓(𝐱^worst_AIA-PSO): the worst objective value obtained using the worst AIA-PSO solution.