Mathematical Definition
Input Domain
The McCormick Function is defined on input range [-1.5<x< 4] and [-3<y<3].
Global Minima
The McCormick Function has one global minimum
fx* = -1.9133 at x* = (-0.547, -1.547).
Description and Features
The McCormick Function is defined on two dimensional spaces. This function is used as a test function in order to evaluate the performance of optimization algorithms such as:
Convergence rate
Precision
Robustness
General Performance.
The McCormick Function is a
Multi-modal
Continuous
Convex
Differentiable
Python Implementation
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import matplotlib.pyplot as plt
import numpy as np
from numpy import sin
from mpl_toolkits import mplot3d
def f(x,y):
return sin(x+y)+((x-y)**2)-1.5*x+2.5*y+1
x=np.linspace(4,-2)
y=np.linspace(4,-4)
x,y=np.meshgrid(x,y)
results=f(x,y)
fig =plt.figure(figsize=(9,9))
axis=fig.gca(projection='3d')
axis.contour3D(x,y,results,450)
axis.set_xlabel('X')
axis.set_ylabel('Y')
axis.set_zlabel('Z')
axis.set_title('McCormick Function')
axis.view_init(50,50)
#plt.contour(x,y,results,15)
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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