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#!/usr/bin/env python
"""
Rosenbrock's function, De Jong's step function, De Jong's quartic function,
and Shekel'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 numpy import sum as numpysum
from numpy import asarray
from math import floor
import random
from math import pow
def rosenbrock(x):
"""
Rosenbrock function:
A modified second De Jong function, Equation (18) of [2]
minimum is f(x)=0.0 at xi=1.0
"""
# ensure that there are 2 coefficients
assert len(x) >= 2
x = asarray(x)
return numpysum(100.0 * (x[1:] - x[:-1] ** 2.0) ** 2.0 + (1 - x[:-1]) ** 2.0)
def step(x):
"""
De Jong's step function:
The third De Jong function, Equation (19) of [2]
minimum is f(x)=0.0 at xi=-5-n where n=[0.0,0.12]
"""
f = 30.0
for c in x:
if abs(c) <= 5.12:
f += floor(c)
elif c > 5.12:
f += 30 * (c - 5.12)
else:
f += 30 * (5.12 - c)
return f
def quartic(x):
"""
De Jong's quartic function:
The modified fourth De Jong function, Equation (20) of [2]
minimum is f(x)=random, but statistically at xi=0
"""
f = 0.0
for j, c in enumerate(x):
f += pow(c, 4) * (j + 1.0) + random.random()
return f
def shekel(x):
"""
Shekel: The modified fifth De Jong function, Equation (21) of [2]
minimum is f(x)=0.0 at x(-32,-32)
"""
A = [-32.0, -16.0, 0.0, 16.0, 32.0]
a1 = A * 5
a2 = reduce(lambda x1, x2: x1 + x2, [[c] * 5 for c in A])
x1, x2 = x
r = 0.0
for i in range(25):
r += 1.0 / (1.0 * i + pow(x1 - a1[i], 6) + pow(x2 - a2[i], 6) + 1e-15)
return 1.0 / (0.002 + r)
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