**Mathematical Definition**

**Input Domain**

The function can be defined on any input domain but it is usually evaluated on xi∈[−500,500] for i=1,…,n. Here, n = 2.

**Global Minima**

The global minima f(x*)=0 are located at x*=(±√i,…,±√i)

**Description and Features**

The function is continuous, not convex, defined on n-dimensional space, multimodal, differentiable, non-separable.

**Python Implementation**

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**import **numpy **as **np
**import **matplotlib.pyplot **as **plt
fig = plt.figure()
ax = fig.gca(projection=**'3d'**)
x = np.arange(-500, 500, 0.1)
y = np.arange(-500, 500, 0.1)
x, y = np.meshgrid(x, y)
res = 0
**for **i **in **range(3):
res = res + ((x ** 2 + y ** 2) -i) ** 2
ax.plot_surface(x, y, res, cmap=**'jet'**)
plt.show()
plt.contour(x,y,res)
plt.show()

**References:**

[1] Jamil, Momin, and Xin-She Yang. "A literature survey of benchmark functions for global optimization problems." *International Journal of Mathematical Modelling and Numerical Optimization* 4.2 (2013): 150-194.

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