def michalewicz(x): # mich.m
x = np.asarray_chkfinite(x)
n = len(x)
j = np.arange(1., n + 1)
t1 = [ria.sin(v) for v in x]
t2 = [ria.sin(j[i] * x[i]**2 / ria.pi()) for i in range(len(x))]
t3 = [t1[i] * t2[i]**((2 * michalewicz_m)) for i in range(len(t1))]
return -sum(t3)
def ackley(x, a=20, b=0.2, c=2 * ria.pi()):
#x = np.asarray_chkfinite(x) # ValueError if any NaN or Inf
#print (x)
n = len(x)
s1 = sum([v**2.0 for v in x])
s2 = sum([ria.cos(c * v) for v in x])
return -a * ria.exp(-b * (s1 / n)**(1.0 / 2.0)) - ria.exp(
s2 / n) + a + ria.exp(1)
def griewank(x, fr=4000):
#x = np.asarray_chkfinite(x)
n = len(x)
j = np.arange(1., n + 1)
s = sum([v**2 for v in x])
v = []
for i in range(len(x)):
v.append(x[i] / ria.sqrt(j[i])) #ria.sqrt
p = prod(([ria.cos(xi) for xi in v]))
return s / fr - p + 1
def nesterov(x):
""" Nesterov's nonsmooth Chebyshev-Rosenbrock function, Overton 2011 variant 2 """
x = np.asarray_chkfinite(x)
x0 = x[:-1]
x1 = x[1:]
t1 = ria.abs(1.0 - qm.midpoint(x[0])) / 4.0
t2 = sum([
ria.abs(qm.midpoint(x1[i] - 2.0 * ria.abs(qm.midpoint(x0[i])) + 1.0))
for i in range(len(x1))
])
return t1 + t2
def perm(x, b=.5):
x = np.asarray_chkfinite(x)
n = len(x)
j = np.arange(1., n + 1)
xbyj = [((ria.abs(x[i])) / j[i]) for i in range(len(x))]
return mean([
mean((j**k + b) * (xbyj**k - 1.0))**2.0 #add media aritmetica em rdm
for k in j / n
])
def levy(x):
x = np.asarray_chkfinite(x)
n = len(x)
z = 1 + (x - 1) / 4.0
t1 = ria.sin(ria.pi() * z[0])**2
t2_1 = [(v - 1)**2 for v in x]
t2_1 = t2_1[:-1]
t2_2 = [(1 + 10 * ria.sin(ria.pi() * v + 1)**2) for v in x]
t2_2 = t2_2[:-1]
t2_3 = [t2_1[i] * t2_2[i] for i in range(len(t2_2))]
t2 = sum(t2_3)
t3 = (z[-1] - 1)**2 * (1 + ria.sin(2 * ria.pi() * z[-1])**2)
return t1 + t2 + t3
def schwefel(x): # schw.m
x = np.asarray_chkfinite(x)
n = len(x)
return 418.9829 * n - sum([v * ria.sin(ria.sqrt(ria.abs(v))) for v in x])
def rastrigin(x): # rast.m
x = np.asarray_chkfinite(x)
n = len(x)
return 10.0 * n + sum(
[v**2.0 - 10.0 * ria.cos(2.0 * ria.pi() * v) for v in x])