A Novel Hybrid Self-Adaptive Bat Algorithm

Table 3

Properties of benchmark functions.

𝑓	𝑓^∗	𝑥^∗	Characteristics	Domain
𝑓1	0.0000	(0,0,…,0)	Highly multimodal	[−600,600]
𝑓2	0.0000	(0,0,…,0)	Highly multimodal	[−15,15]
𝑓3	0.0000	(1,1,…,1)	Several local optima	[−15,15]
𝑓4	0.0000	(0,0,…,0)	Highly multimodal	[−32.768,32.768]
𝑓5	0.0000	(0,0,…,0)	Highly multimodal	[−500,500]
𝑓6	0.0000	(0,0,…,0)	Unimodal, convex	[−600,600]
𝑓7	−1.0000	(𝜋,𝜋,…,𝜋)	Several local optima	[−2𝜋,2𝜋]
𝑓8	−1.8013^1	(2.20319,1.57049)^1	Several local optima	[0,𝜋]
𝑓9	0.0000	(0,0,…,0)	Several local optima	[−2𝜋,2𝜋]
𝑓10	0.0000	(0,0,…,0)	Unimodal	[−5,10]

1Valid for 2-dimensional parameter space.