Cloud Model Bat Algorithm

Table 1

Benchmarking test functions.

Benchmarks functions	Functions expression	Exact value	𝑥∗	Search space
𝑓1: Sphere	𝑓(𝑥)=∑^𝑛𝑖=1𝑥^2𝑖	𝑓min=0	(0,0,…,0)	[−10, 10]
𝑓2: Schwefel	𝑓(𝑥)=∑^𝑛𝑖=1𝑥𝑖+∏^𝑛𝑖=1𝑥𝑖	𝑓min=0	(0,0,…,0)	[−10, 10]
𝑓3: Rosenbrock	𝑓(𝑥)=∑^𝑛𝑖=1(𝑥𝑖−1)^2+100𝑥𝑖+1−𝑥𝑖^22	𝑓min=0	(1,1,…,1)	[−2.408, 2.408]
𝑓4: Ackley	𝑓(𝑥)=20+𝑒−20exp−0.21𝑛×∑^𝑛𝑖=1𝑥^2𝑖−exp−0.21𝑛×∑^𝑛𝑖=1cos2𝜋𝑥𝑖	𝑓min=0	(0,0,…,0)	[−30, 30]
𝑓5: Griewangk	1𝑓(𝑥)=×4000^𝑛𝑖∑=1𝑥^2𝑖−∏^𝑛𝑖=1𝑥cos^𝑖√𝑖+1	𝑓min=0	(0,0,…,0)	[−600, 600]
𝑓6: Rastrigin	𝑓(𝑥)=10𝑛+∑^𝑛𝑖=1𝑥^2𝑖−10cos2𝜋𝑥𝑖	𝑓min=0	(0,0,…,0)	[−5.12, 5.12]
𝑓7: Shubert	𝑓𝑥,𝑦=∑^5𝑖=1𝑖cos(𝑖+(𝑖+1)𝑥)⋅∑^5𝑖=1𝑖cos𝑖+(𝑖+1)𝑦	𝑓min≈−186.7309	—	[−10, 10]
𝑓8: Easom	𝑓(𝑥,𝑦)=−cos(𝑥)cos𝑦exp−(𝑥−𝜋)^2+𝑦−𝜋^2	𝑓min=−1	(𝜋,𝜋)	[−10, 10]