Function Equation Dimension (n) Search Space (xmin, xmax) Global Minimum
Paraboloid \(f\left(\ x\ \right)=x_{1}^{2}+x_{2}^{2}\) 2 [-100,100] 0
Sphere \(f\left(\ x\ \right)=\sum_{i=1}^{n}x_{i}^{2}\) 20,000 [-100, 100] 0
Rosenbrock \(f\left(x\right)=\sum_{i=1}^{n-1}\left[100\left(x_{i+1}-x_{i}^{2}\right)^{2}+\left(x_{i}-1\right)^{2}\right]\) 20,000 [-30, 30] 0
Rastrigin \(f\left(x\right)=\sum_{i=1}^{n}\left[x_{i}^{2}-10\cos\left(2\pi x_{i}\right)+10\right]\) 20,000 [-5.12, 5.12] 0
Griewank \(f\left(x\right)=\frac{1}{4000}\sum_{i=1}^{n}\left[x_{i}^{2}-\prod_{i=1}^{n}{\cos\left(\frac{x_{i}}{\sqrt{i}}+1\right)}\right]\) 20,000 [-600, 600] 0
Shaffer f6 \(f\left(x\right)=0.5-\frac{\left(\sin\sqrt{x_{1}^{2}+x_{2}^{2}}\right)^{2}-0.5}{\left[1+0.001\left(x_{1}^{2}+x_{2}^{2}\right)\right]^{2}}\) 2 [-100, 100] 0
Alpine \(f\left(x\right)=\sum_{i=1}^{n}\left[x_{i}\sin\left(x_{i}\right)+0.1x_{i}\right]\) 20,000 [-10, 10] 0
Brown \(f\left(x\right)=\sum_{i=1}^{n-1}\left[\left(x_{i}^{2}\right)^{x_{i+1}^{2}+1}+\left(x_{i+1}^{2}\right)^{x_{i}^{2}+1}\right]\) 20,000 [-1, 1] 0
Chung Reynolds \(f\left(x\right)=\left(\sum_{i=1}^{n}\left[x_{i}^{2}\right]\right)^{2}\) 20,000 [-100, 100] 0
Dixon Price \(f\left(x\right)=\left(x_{1}-1\right)^{2}+\sum_{i=2}^{n}\left[i\left(2x_{i}^{2}-x_{i-1}\right)^{2}\right]\) 20,000 [-10, 10] 0
Exponential \(f\left(x\right)=-exp\left(-0.5\sum_{i=1}^{n}\left[x_{i}^{2}\right]\right)\) 20,000 [-1, 1] -1
Salomon \(f\left(x\right)=1-\cos\left(2\pi\sqrt{\sum_{i=1}^{n}\left[x_{i}^{2}\right]}\right)+0.1\sqrt{\sum_{i=1}^{n}\left[x_{i}^{2}\right]}\) 20,000 [-100, 100] 0
Schumer Steiglitz \(f\left(x\right)=\sum_{i=1}^{n}\left[x_{i}^{4}\right]\) 20,000 [-100, 100] 0
Sum of Powers \(f\left(x\right)=\sum_{i=1}^{n}\left[\left|x_{i}\right|^{i+1}\right]\) 20,000 [-1, 1] 0
Sum of Squares \(f\left(x\right)=\sum_{i=1}^{n}\left[ix_{i}^{2}\right]\) 20,000 [-1, 1] 0
Zakharov \(f\left(x\right)=\sum_{i=1}^{n}\left[x_{i}^{2}\right]+\left(\sum_{i=1}^{n}\left[0.5ix_{i}\right]\right)^{2}+\left(\sum_{i=1}^{n}\left[0.5ix_{i}\right]\right)^{4}\) 20,000 [-10, 10] 0