A Simple and Efficient Artificial Bee Colony Algorithm

Table 1

Benchmark functions used in the experiments.

Name	Function	Range	Opt
Sphere	𝑓1=∑^𝐷𝑖=1𝑥^2𝑖	[−100,100]	0
Schwefel 2.22	𝑓2=∑^𝐷𝑖=1𝑥𝑖+∏^𝐷𝑖=1𝑥𝑖	[−10, 10]	0
Schwefel 1.2	𝑓3=∑^𝐷𝑖=1∑^𝑖𝑗=1𝑥𝑗^2	[−100, 100]	0
Schwefel 2.21	𝑓4=max𝑖𝑥𝑖,1≤𝑖≤𝐷	[−100, 100]	0
Rosenbrock	𝑓5=∑^𝐷−1𝑖=1100(𝑥𝑖+1−𝑥^2𝑖)^2+(𝑥𝑖−1)^2	[−30, 30]	0
Step	𝑓6=∑^𝐷𝑖=1𝑥𝑖+0.5^2	[−100, 100]	0
Quartic with noise	𝑓7=∑^𝐷𝑖=1𝑖𝑥^4𝑖+rand[0,1)	[−1.28, 1.28]	0
Schwefel 2.26	𝑓8=∑^𝐷𝑖=1−𝑥𝑖sin|𝑥𝑖|	[−500, 500]	−12569.5
Rastrigin	𝑓9=∑^𝐷𝑖=1[𝑥^2𝑖−10cos(2𝜋𝑥𝑖)+10]	[−5.12, 5.12]	0
Ackley	𝑓10=−20exp−0.21𝐷∑^𝐷𝑖=1𝑥^2𝑖1−exp𝐷∑^𝐷𝑖=1cos2𝜋𝑥𝑖+20+𝑒	[−32, 32]	0
Griewank	𝑓11=1∑4000^𝐷𝑖=1𝑥^2𝑖−∏^𝐷𝑖=1𝑥cos(^𝑖√𝑖)+1	[−600, 600]	0
Penalized	f 12  =𝜋𝐷{10sin^2(3𝜋𝑦𝑖)+∑^𝐷−1𝑖=1(𝑦𝑖−1)^2[1+10sin^2(𝜋𝑦𝑖+1)]; +(𝑦𝐷−1)^2}+∑^𝐷𝑖=1𝑢(𝑥𝑖,5,100,4)	[−50,50]	0