A Multistrategy Optimization Improved Artificial Bee Colony Algorithm

Table 1

Dimension, search space, and optimal value of test functions.

Function	Mathematical representation	Dimension (𝐷)	Range of search (𝑆)	Theoretical optimum 𝑓min
Sphere (𝑓1)	𝑓1(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖	50	[−100, 100]^𝐷	0
Rosenbrock (𝑓2)	𝑓2(𝑥)=∑^𝐷𝑖=1100𝑥𝑖+1−𝑥^2𝑖^2+𝑥𝑖−1^2	50	[−30, 30]^𝐷	0
Griewank (𝑓3)	𝑓31(𝑥)=4000^𝐷𝑖∑=1𝑥^2𝑖−∏^𝐷𝑖=1𝑥cos^𝑖√𝑖+1	50	[−600, 600]^𝐷	0
Rastrigin (𝑓4)	𝑓4(𝑥)=∑^𝐷𝑖=1𝑥^2𝑖−10cos(2𝜋𝑥𝑖)+10	50	[−5.12, 5.12]^𝐷	0
Ackley (𝑓5)	𝑓5(𝑥)=−20exp−0.21𝐷^𝐷𝑖∑=1𝑥^2𝑖1−exp−0.2𝐷^𝐷𝑖∑=1cos(2𝜋𝑥𝑖)+20+𝑒	50	[−30, 30]^𝐷	0
Levi11 (𝑓6)	𝑓6(𝑥)=sin(3𝜋𝑥1)^2+(𝑥1−1)^2(1+sin(3𝜋𝑥1)^2)+(𝑥2−1)^2(1+sin(2𝜋𝑥2)^2)	50	[−10, 10]^𝐷	0
Schwefel’s problem (𝑓7)	𝑓7(𝑥)=∑^𝐷𝑖=1𝑥𝑖+∏^𝐷𝑖=1𝑥𝑖	50	[−500, 500]^𝐷	−837.9658
Alpine (𝑓8)	𝑓(𝑥)=∑^𝐷𝑖=1𝑥𝑖sin(𝑥𝑖)+0.1𝑥𝑖	50	[−100, 100]^𝐷	0
Cross (𝑓9)	𝑓10(𝑥)=sin(𝑥1)sin(𝑥2)𝑒^|100−𝑥21+𝑥22/𝜋|+1	2	[−10, 10]^𝐷	0
Schaffer's F6 (𝑓10)	𝑓9(𝑥)=0.5+sin^2𝑥^21+𝑥^22−0.5(1+0.001(𝑥^21+𝑥^22))^2	2	[−100, 100]^𝐷	0