Mathematical Definition
Input Domain
The function is usually evaluated on the hypercube xi ∈ [-5, 5], for all i = 1, 2.
Global Minima
f(x*)=0, at x* =(0, 0).
Description
The function is continuous.
The function is not convex.
The function is defined on 2-dimensional space.
The function is multimodal.
The function is differentiable.
The function is non-separable.
Python Implementation
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# Author: Dhanishtha Sharma
import sympy
import math
from sympy import symbols
from sympy import *
from sympy.plotting import plot3d
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
#%matplotlib notebook
plt.rcParams['figure.figsize'] = (6,4)
plt.rcParams['figure.dpi']=150
fig=plt.figure()
ax=fig.add_subplot(111,projection='3d')
x1,x2=symbols('x1 x2')
plot3d((2*(x1**2)-1.05*(x1**4)+((x1**6)/6)+(x1*x2)+(x2**2)),(x1,-5,5),(x2,-5,5))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.