Problem

Function

CEC01

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D{\left({\displaystyle \sum _{j=1}^i{x}_j}\right)}^2}\\ \text{s}\text{.t}\text{.}g\left(x\right)={\displaystyle \sum _{i=1}^D\left[x_i^2-5000\cos \left(0.1\pi x_i\right)-4000\right]}\le 0\end{array}$

CEC02

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D{\left({\displaystyle \sum _{j=1}^{i}M{x}_j}\right)}^2}\\ \text{s}\text{.t}\text{.}g\left(x\right)={\displaystyle \sum _{i=1}^D\left[{\left(M{x}_i\right)}^2-5000\cos \left(0.1\pi M{x}_i\right)-4000\right]}\le 0\end{array}$

CEC03

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]}\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)=-{\displaystyle \sum _{i=1}^D{x}_i\sin \left(2x_i\right)}\le 0,g_2\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i\sin \left(2x_i\right)}\le 0\end{array}$

CEC04

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^{D-1}\left[100{\left(x_i^2-x_{i+1}\right)}^2+{\left(x_i^2-1\right)}^2\right]}\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)={\displaystyle \sum _{i=1}^D\left[{\left(M_1{x}_i\right)}^2-50\cos \left(2\pi M_1{x}_i\right)-40\right]}\le 0\\ g_2\left(x\right)={\displaystyle \sum _{i=1}^D\left[{\left(M_2{x}_i\right)}^2-50\cos \left(2\pi M_2{x}_i\right)-40\right]}\le 0\end{array}$

CEC05

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]}\\ \text{s}\text{.t}\text{.}{h}_1\left(x\right)=-{\displaystyle \sum _{i=1}^D{x}_i\sin \left(x_i\right)}=0\\ h_2\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i\sin \left(\pi x_i\right)}=0\\ h_3\left(x\right)=-{\displaystyle \sum _{i=1}^D{x}_i\cos \left(x_i\right)}=0\\ h_4\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i\cos \left(\pi x_i\right)}=0\\ h_5\left(x\right)={\displaystyle \sum _{i=1}^D\left(x_i\sin \left(2\sqrt{\left|x_i\right|}\right)\right)}=0\\ h_6\left(x\right)=-{\displaystyle \sum _{i=1}^D\left(x_i\sin \left(2\sqrt{\left|x_i\right|}\right)\right)}=0\end{array}$

CEC06

$\begin{array}{l}\min f\left(x\right)=\max \left(x_i\right)y_l=x_{2l-1},w_l=x_{2l}\text{where}l=1,\cdots ,D/2\\ \text{s}\text{.t}\text{.}{h}_1\left(x\right)={\displaystyle \sum _{i=1}^{D/2}{\left({\displaystyle \sum _{j=1}^i{y}_j}\right)}^2}=0\\ h_2\left(x\right)={\displaystyle \sum _{i=1}^{D/2}{\left({\displaystyle \sum _{j=1}^i{w}_j}\right)}^2}=0\end{array}$

CEC07

$\begin{array}{l}\min f\left(x\right)=\max \left(x_i\right)y_l=x_{2l-1},w_l=x_{2l}\text{where}l=1,\cdots ,D/2\\ \text{s}\text{.t}\text{.}g\left(x\right)={\displaystyle \prod _{i=1}^{D/2}{w}_i}\le 0\\ h\left(x\right)={\displaystyle \sum _{i=1}^{D/2}{\left(y_i^2-y_{i+1}\right)}^2}=0\end{array}$

CEC08

$\begin{array}{l}\min f\left(x\right)=\max \left(x_i\right)\\ \text{s}\text{.t}\text{.}{h}_1\left(x\right)={\displaystyle \sum _{i=1}^D{\left({\displaystyle \sum _{j=1}^i{x}_j}\right)}^2}=0\\ h_2\left(x\right)={\displaystyle \sum _{i=1}^{D-1}{\left(x_i-x_{i+1}\right)}^2}=0\end{array}$

CEC09

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i}\\ \text{s}\text{.t}\text{.}g\left(x\right)={\displaystyle \prod _{i=1}^D{x}_i}\le 0\\ h\left(x\right)={\displaystyle \sum _{i=1}^{D-1}{\left(x_i^2-x_{i+1}\right)}^2}=0\end{array}$

CEC10

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^{D-1}\left(100{\left(x_i^2-x_{i+1}\right)}^2+{\left(x_i-1\right)}^2\right)}\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)={\displaystyle \sum _{i=1}^D\left(x_i^2-10\cos \left(2\pi x_i\right)+10\right)-100}\le 0\\ g_2\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i}-2D\le 0\\ g_3\left(x\right)=5-{\displaystyle \sum _{i=1}^D{x}_i}\le 0\end{array}$

CEC11

$\begin{array}{l}\min f\left(x\right)=\max \left\{\left|x_i\right|,1\le i\le D\right\}\\ \text{s}\text{.t}\text{.}g\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i^2-100D}\le 0\\ h\left(x\right)=\cos f\left(x\right)+\sin f\left(x\right)=0\end{array}$

CEC12

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D\left|x_i\right|}\\ \text{s}\text{.t}\text{.}g\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i^2-100D}\le 0\\ h\left(x\right)={\left(\cos f\left(x\right)+\sin f\left(x\right)\right)}^2-\exp \left(\cos f\left(x\right)+\sin f\left(x\right)\right)-1+\exp \left(1\right)=0\end{array}$

CEC13

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D\left(z_i^2-10\cos \left(2\pi z_i\right)+10\right)},z_i^2=\{\begin{array}{l}{x}_i^2,\text{if}\left|x_i^2\right|<0.5\\ 0.5round\left(2x_i\right),\text{otherwise}\end{array}\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)=1-{\displaystyle \sum _{i=1}^D\left|x_i\right|}\le 0\\ g_2\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i^2}-100D\le 0\\ h\left(x\right)={\displaystyle \sum _{i=1}^{D}100{\left(x_i^2-x_{i+1}\right)}^2}+{\displaystyle \prod _{i=1}^D{\sin }^2\left(x_i-1\right)\pi }=0\end{array}$

CEC14

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^{D-1}g\left(x_i,x_{i+1}\right)}+g\left(x_D,x_1\right),g\left(x_i,x_{i+1}\right)=0.5+\frac{{\sin }^2\left(\sqrt{x_i^2+x_{i+1}^2}\right)-0.5}{{\left(1+0.001\sqrt{x_i^2+x_{i+1}^2}\right)}^2}\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)={\cos }^2\left({\displaystyle \sum _{i=1}^D{x}_i}\right)-0.25\cos \left({\displaystyle \sum _{i=1}^D{x}_i}\right)-0.125\le 0\\ g_2\left(x\right)=\exp \left(\cos \left({\displaystyle \sum _{i=1}^D{x}_i}\right)\right)-\exp \left(0.25\right)\le 0\end{array}$

CEC15

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D\left[y_i^2-10\cos \left(2\pi y_i\right)+10\right]},y=Mx\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)=4-{\displaystyle \sum _{i=1}^D\left|y_i\right|}\le 0\\ g_2\left(x\right)={\displaystyle \sum _{i=1}^{D}y}-4\le 0\end{array}$

CEC16

$\begin{array}{l}\min f\left(x\right)={\displaystyle \sum _{i=1}^D\left[100{\left(y_i^2-x_{i+1}\right)}^2+{\left(y_i-1\right)}^2\right]},y=Mx\\ \text{s}\text{.t}\text{.}{g}_1\left(x\right)={\displaystyle \sum _{i=1}^D\left(y_i^2-10\cos \left(2\pi y_i\right)+10\right)}\le 0\\ g_2\left(x\right)={\displaystyle \sum _{i=1}^D{y}_i}-2D\le 0\\ g_2\left(x\right)=5-{\displaystyle \sum _{i=1}^D{y}_i}\le 0\end{array}$