A Novel Hybrid Self-Adaptive Bat Algorithm

Table 2

Definitions of benchmark functions.

𝑓	Function name	Definition
𝑓1	Griewangk’s function	𝑓(𝐱)=−∏^𝑛𝑖=1𝑥cos^𝑖√𝑖+∑^𝑛𝑖=1𝑥^2𝑖4000+1
𝑓2	Rastrigin’s function	𝑓(𝐱)=𝑛∗10+∑^𝑛𝑖=1(𝑥^2𝑖−10cos(2𝜋𝑥𝑖))
𝑓3	Rosenbrock’s function	𝑓(𝐱)=∑^𝑛−1𝑖=1100𝑥𝑖+1−𝑥^2𝑖^2+(𝑥𝑖−1)^2
𝑓4	Ackley’s function	𝑓(𝐱)=∑^𝑛−1𝑖=120+𝑒^−20𝑒^−0.20.5(𝑥2𝑖+1+𝑥2𝑖)−𝑒^0.5(cos(2𝜋𝑥𝑖+1)+cos(2𝜋𝑥𝑖))
𝑓5	Schwefel’s function	𝑓(𝐱) =  418.9829∗𝐷−∑^𝐷𝑖=1𝑥𝑖sin𝑥𝑖
𝑓6	De Jong’s sphere function	𝑓(𝐱)=∑^𝐷𝑖=1𝑥^2𝑖
𝑓7	Easom’s function	𝑓(𝐱)=−(−1)∏^𝐷𝐷𝑖=1cos^2𝑥𝑖exp−∑^𝐷𝑖=1𝑥𝑖−𝜋^2
𝑓8	Michalewicz’s function	𝑓(𝐱)=−∑^𝐷𝑖=1sin(𝑥𝑖)sin𝑖𝑥^2𝑖𝜋^2⋅10
𝑓9	Xin-She Yang’s function	𝑓(𝐱)=∑^𝐷𝑖=1𝑥𝑖exp−∑^𝐷𝑖=1sin𝑥^2𝑖
𝑓10	Zakharov’s function	𝑓(𝐱)=∑^𝐷𝑖=1𝑥^2𝑖+12^𝐷𝑖∑=1𝑖𝑥𝑖^2+12^𝐷𝑖∑=1𝑖𝑥𝑖^4