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#!/usr/bin/env python
"""
Griewangk'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 six.moves import reduce
from math import cos, sqrt
def griewangk(coeffs):
"""
Griewangk function: a multi-minima function, Equation (23) of [2]
minimum is f(x)=0.0 at xi=0.0
"""
# ensure that there are 10 coefficients
x = [0]*10
x[:len(coeffs)]=coeffs
term1 = sum([xi*xi for xi in x])/4000
term2 = prod([cos(xi/sqrt(i+1.)) for i,xi in enumerate(x)])
return term1 - term2 + 1
prod = lambda x: reduce(lambda a,b: a*b, x, 1.)
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