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#!/usr/bin/env python
"""
Corana's function
References::
[1] Storn, R. and Price, K. Differential Evolution - A Simple and Efficient
Heuristic for Global Optimization over Continuous Spaces. Journal of Global
Optimization 11: 341-359, 1997.
[2] Storn, R. and Price, K.
(Same title as above, but as a technical report.)
http://www.icsi.berkeley.edu/~storn/deshort1.ps
"""
from math import pow, floor, copysign
def corana1d(x):
"""Corana in 1D; coeffs = (x,0,0,0)"""
return corana4d([x[0], 0, 0, 0])
def corana2d(x):
"""Corana in 2D; coeffs = (x,0,y,0)"""
return corana4d([x[0], 0, x[1], 0])
def corana3d(x):
"""Corana in 3D; coeffs = (x,0,y,z)"""
return corana4d([x[0], 0, x[1], x[2]])
def corana4d(x):
"""
evaluates the Corana function on [x0,x1,x2,x3]
minimum is f(x)=0.0 at xi=0.0
"""
d = [1., 1000., 10., 100.]
r = 0
for xj,dj in zip(x,d):
zj = floor( abs(xj/0.2) + 0.49999 ) * copysign(0.2,xj)
if abs(xj-zj) < 0.05:
r += 0.15 * pow(zj - copysign(0.05,zj), 2) * dj
else:
r += dj * xj * xj
return r
# End of file
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