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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 functools 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 + 1.0)) for i, xi in enumerate(x)])
return term1 - term2 + 1
prod = lambda x: reduce(lambda a, b: a * b, x, 1.0)
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