函数名称

公式

问题维度

搜索空间

最优值

Sphere

$F_1\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i^2}$

30

[−100, 100]

0

Schwefel 1.2

$F_2\left(x\right)={\displaystyle \sum _{i=1}^D{\left({\displaystyle \sum _{j=1}^i{x}_j^2}\right)}^2}$

30

[−100, 100]

0

Rosenbrock

$F_3\left(x\right)={\displaystyle \sum _{j=1}^{D-1}\left[100{\left(x_{i+1}-x_i^2\right)}^2+{\left(x_i-1\right)}^2\right]}$

30

[−30, 30]

0

Schwefel 2.22

$F_4\left(x\right)={\displaystyle \sum _{i=1}^D\left|x_i\right|}+{\displaystyle \prod _{i=1}^D\left|x_i\right|}$

30

[−10, 10]

0

Quartic Function i.e. Noise

$F_5\left(x\right)={\displaystyle \sum _{i=1}^{D}i{x}_i^4}+random\left[0,1\right)$

30

[−1.28, 1.28]

0

Rastrigin

$F_6\left(x\right)={\displaystyle \sum _{i=1}^D{x}_i^2}-10\cos \left(2\pi x_i\right)+10$

30

[−5.12, 5.12]

0

Ackley

$F_7\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^D{x}_i^2}}\right)-\exp \left(\frac{1}{D}{\displaystyle \sum _{i=1}^D\cos \left(2\pi x_i\right)}\right)+20+e$

30

[−32, 32]

0

Griewank

$F_8\left(x\right)=\frac{1}{4000}{\displaystyle \sum _{i=1}^D{x}_i^2}-{\displaystyle \prod _{i=1}^D\cos \left(\frac{x_i}{\sqrt{i}}\right)}+1$

30

[−600, 600]

0

Schwefel

$F_9\left(x\right)=418.9829\times D-{\displaystyle \sum _{i=1}^D{x}_i\sin \left(\sqrt{\left|x_i\right|}\right)}$

30

[−500, 500]

0