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#!/usr/bin/env python
"""
Zimmermann'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
"""
def zimmermann(x):
"""
Zimmermann function: a non-continuous function, Equation (24-26) of [2]
minimum is f(x)=0.0 at x=(7.0,2.0)
"""
x0, x1 = x # must provide 2 values (x0,y0)
f8 = 9 - x0 - x1
c0, c1, c2, c3 = 0, 0, 0, 0
if x0 < 0:
c0 = -100 * x0
if x1 < 0:
c1 = -100 * x1
xx = (x0 - 3.0) * (x0 - 3) + (x1 - 2.0) * (x1 - 2)
if xx > 16:
c2 = 100 * (xx - 16)
if x0 * x1 > 14:
c3 = 100 * (x0 * x1 - 14.0)
return max(f8, c0, c1, c2, c3)
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