Table 4.

The test functions of CEC 2015.

Function	Formulation	Limits	Minimum
Type: unimodal
Sphere	f 1(x)=∑i=1Dxi2	x i ∈ [−100,100]	$f_1\left(\stackrel{⟶}{0}\right)=0$
Schwefel's problem 2.22	f 2(x)=∑i=1D|xi|+∏i=1D|xi|	x i ∈ [−10,10]	$f_2\left(\stackrel{⟶}{0}\right)=0$
Rosenbrock	f 3(x)=∑i=1P−1[100(xi+1 − xi)2+(1 − xi)2]	x i ∈ [−30,30]	$f_3\left(\stackrel{⟶}{0}\right)=0$
High conditioned elliptic	f 4(x)=∑i=1D(106)((i − 1)/(D − 1))xi2	x i ∈ [−100,100]	$f_4\left(\stackrel{⟶}{0}\right)=0$
Dixon-Price	f 5(x)=(x1 − 1)2+∑i=2Di(2xi2 − xi−1)2	x i ∈ [−10,10]	$f_5\left(\stackrel{⟶}{x_i}\right)=0$
Type: multimodal
Ackley	$f_6\left(x\right)=-20\exp \left(-0.2\sqrt{\left(1/P\right){\displaystyle {\sum }_{i=1}^P{x}_i^2}}\right)-\exp \left(\left(1/P\right){\displaystyle {\sum }_{i=1}^P\cos \left(2\pi x_i\right)}\right)+20+e$	x i ∈ [−30,30]	$f_6\left(\stackrel{⟶}{0}\right)=0$
Rastrigin	f 7(x)=∑i=1P(xi2 − 10cos(2πxi)+10)	x i ∈ [−5.12, 5.12]	$f_7\left(\stackrel{⟶}{0}\right)=0$
Griewank	$f_8\left(x\right)=\left(1/4000\right)\left({\displaystyle {\sum }_{i=1}^P{x}_i^2}\right)-\left[{\displaystyle {\prod }_{i=1}^P\cos \left(x_i|/|\sqrt{i}\right)}\right]+1$	x i ∈ [−600,600]	$f_8\left(\stackrel{⟶}{0}\right)=0$
Levy	f 9(x)=sin2(πω1)+∑i=1D−1(ωi − 1)2[1+10sin2(πωi+1)]+(ωD − 1)2[1+sin2(2πωD)];  ωi=1+((xi − 1)/4)	x i ∈ [−10,10]	$f_9\left(\stackrel{⟶}{1}\right)=0$
HappyCat	f 10(x)=|∑i=1Dxi2−D|1/4+((0.5∑i=1Dxi2+∑i=1Dxi)/D)+0.5	x i ∈ [−5,5]	$f_{10}\left(\stackrel{⟶}{-1}\right)=0$