def multifidelity_hartmann6_levels():
dim = 6
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f_H(x):
alpha = np.array([1.0, 1.2, 3.0, 3.2])
A = np.array([[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14]])
P = 1e-4 * np.array([[1312, 1696, 5569, 124, 8283, 5886],
[2329, 4135, 8307, 3736, 1004, 9991],
[2348, 1451, 3522, 2883, 3047, 6650],
[4047, 8828, 8732, 5743, 1091, 381]])
arg = np.dot(A, (x-P).T**2)
y = -np.dot(alpha, np.diag(np.exp(-arg)))
return y
def f_L(x, dm):
alpha = np.array([1.0, 1.2, 3.0, 3.2])
delta = np.array([0.01, -0.01, -0.1, 0.1])
alpha2 = alpha + dm * delta
A = np.array([[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14]])
P = 1e-4 * np.array([[1312, 1696, 5569, 124, 8283, 5886],
[2329, 4135, 8307, 3736, 1004, 9991],
[2348, 1451, 3522, 2883, 3047, 6650],
[4047, 8828, 8732, 5743, 1091, 381]])
arg = np.dot(A, (x-P).T**2)
y = -np.dot(alpha, np.diag(np.exp(-arg)))
return y
return (f_L, f_H), p_x, dim, lb, ub
def multifidelity_hartmann3():
dim = 3
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f_H(x):
alpha = np.array([1.0, 1.2, 3.0, 3.2])
A = np.array([[3, 10, 30],
[0.1, 10, 35],
[3, 10, 30],
[0.1, 10, 35]])
P = 1e-4 * np.array([[3689, 1170, 2673],
[4699, 4387, 7470],
[1091, 8732, 5547],
[381, 5743, 8828]])
arg = np.dot(A, (x-P).T**2)
y = -np.dot(alpha, np.diag(np.exp(-arg)))
return y
def f_L(x):
alpha = np.array([1.0, 1.2, 3.0, 3.2])
delta = np.array([0.01, -0.01, -0.1, 0.1])
alpha2 = alpha + (3 - 2) * delta
A = np.array([[3, 10, 30],
[0.1, 10, 35],
[3, 10, 30],
[0.1, 10, 35]])
P = 1e-4 * np.array([[3689, 1170, 2673],
[4699, 4387, 7470],
[1091, 8732, 5547],
[381, 5743, 8828]])
arg = np.dot(A, (x-P).T**2)
y = -np.dot(alpha2, np.diag(np.exp(-arg)))
return y
return (f_L, f_H), p_x, dim, lb, ub
def step_function():
dim = 1
lb = -np.ones(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f(x):
return np.heaviside(x, 0.5)[0]
return f, p_x, dim, lb, ub
def himmelblau():
dim = 2
lb = np.array([-6.0, -6.0])
ub = np.array([6.0, 6.0])
p_x = uniform_prior(lb, ub)
def f(x):
x1, x2 = x[0], x[1]
y = (x1**2 + x2 - 11)**2 + (x1 + x2**2 - 7)**2
return y
return f, p_x, dim, lb, ub
def singlefidelity_singer_cox():
dim = 4
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f(x):
x1, x2, x3, x4 = x[0], x[1], x[2], x[3]
y = 1/2.*(np.sqrt(x1**2 + (x2 + x3**2)*x4) - x1) + (x1 + 3*x4)*np.exp(1 + np.sin(x3))
return -y # maximize y -- > minimize -y
return f, p_x, dim, lb, ub
def rosenbrock():
dim = 2
lb = np.array([-1.0, -1.0])
ub = np.array([0.5, 1.0])
p_x = uniform_prior(lb, ub)
def f(x):
y = 74.0 + 100.0 * (x[1] - x[0] ** 2) ** 2 + (1.0 - x[0]) ** 2
y -= 400.0 * np.exp(-((x[0] + 1.0) ** 2 + (x[1] + 1.0) ** 2) / 0.1)
return y
return f, p_x, dim, lb, ub
def bukin():
dim = 2
lb = np.array([-15.0, -3.0])
ub = np.array([-5.0, 3.0])
p_x = uniform_prior(lb, ub)
def f(x):
x1, x2 = x[0], x[1]
y = 100 * np.sqrt( np.abs(x2-0.01*x1**2) ) + 0.01 * np.abs(x1+10)
return y
return f, p_x, dim, lb, ub
def bird():
dim = 2
lb = -2.0*np.pi*np.ones(dim)
ub = 2.0*np.pi*np.ones(dim)
p_x = uniform_prior(lb, ub)
def f(x):
x1, x2 = x[0], x[1]
y = np.sin(x1) * np.exp( (1-np.cos(x2))**2 ) \
+ np.cos(x2) * np.exp( (1-np.sin(x1))**2 ) + (x1-x2)**2
return y
return f, p_x, dim, lb, ub
def singlefidelity_camelback():
dim = 2
lb = np.array([-2.0, -1.0])
ub = np.array([2.0, 1.0])
p_x = uniform_prior(lb, ub)
def f_H(x):
x1, x2 = x[0], x[1]
y = (4.0 - 2.1*x1**2 + x1**4/3.)*x1**2 + x1*x2 + (-4. + 4.*x2**2)*x2**2
return y
return f_H, p_x, dim, lb, ub
def ackley(dim=2):
lb = -32.768*np.ones(dim)
ub = 32.768*np.ones(dim)
p_x = uniform_prior(lb, ub)
def f(x):
a = 20
b = 0.2
c = 2*np.pi
return - a * np.exp( -b * np.sqrt(np.sum(x**2)/dim) ) \
- np.exp( np.sum(np.cos(c*x))/dim ) \
+ a + np.exp(1.0)
return f, p_x, dim, lb, ub
def ursem_waves():
dim = 2
lb = np.array([-0.9, -1.2])
ub = np.array([1.2, 1.2])
p_x = uniform_prior(lb, ub)
def f(x):
x1, x2 = x[0], x[1]
u = -0.9*x1**2
v = (x2**2 - 4.5*x2**2) * x1 * x2
w = 4.7*np.cos(3*x1 - x2**2 * (2+x1)) * np.sin(2.5*np.pi*x1)
return u + v + w
return f, p_x, dim, lb, ub
def heterogeneous_forrester():
dim = 2
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f_H(x):
x1, x2 = x[0], x[1]
y = (6.0*x1-2.0)**2 * np.sin(12.0*x1-4.0)
return y
def f_L(x):
y = 0.5*f_H(x)
return y
return (f_L, f_H), p_x, dim, lb, ub
def forrester():
dim = 1
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f_H(x):
x = x.flatten()
y = (6.0*x-2.0)**2 * np.sin(12.0*x-4.0)
return y[0]
def f_L(x):
x = x.flatten()
y = 0.5*f_H(x) + 10.0*(x-0.5) - 5.0
return y[0]
return (f_L, f_H), p_x, dim, lb, ub
def multifidelity_singer_cox():
dim = 4
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f_H(x):
x1, x2, x3, x4 = x[0], x[1], x[2], x[3]
y = 1/2.*(np.sqrt(x1**2 + (x2 + x3**2)*x4) - x1) + (x1 + 3*x4)*np.exp(1 + np.sin(x3))
return -y # maximize y -- > minimize -y
def f_L(x):
x1, x2, x3, x4 = x[0], x[1], x[2], x[3]
y = (1 + np.sin(x1)/10.) * (-f_H(x)) - 2*x1**2 + x2**2 + x3**2 + 0.5
return -y
return (f_L, f_H), p_x, dim, lb, ub
def multifidelity_camelback():
dim = 2
lb = np.array([-2.0, -1.0])
ub = np.array([2.0, 1.0])
p_x = uniform_prior(lb, ub)
def f_H(x):
x1, x2 = x[0], x[1]
y = (4.0 - 2.1*x1**2 + x1**4/3.)*x1**2 + x1*x2 + (-4. + 4.*x2**2)*x2**2
return y
def f_L(x):
x1, x2 = x[0] + 0.1, x[1] - 0.1
z = (4.0 - 2.1*x1**2 + x1**4/3.)*x1**2 + x1*x2 + (-4. + 4.*x2**2)*x2**2
y = 0.75*f_H(x) + 0.375*z - 0.125
return y
return (f_L, f_H), p_x, dim, lb, ub
def branin():
dim = 2
lb = np.array([-5.0, 0.0])
ub = np.array([10.0, 15.0])
p_x = uniform_prior(lb, ub)
def f(x):
a = 1.0
b = 5.1 / (4*np.pi**2)
c = 5 / np.pi
r = 6
s = 10
t = 1 / (8*np.pi)
x1, x2 = x[0], x[1]
y = a * (x2 - b*x1**2 + c*x1 -r)**2 + s * (1-t) * np.cos(x1) + s
return y
return f, p_x, dim, lb, ub
def jump_forrester():
dim = 1
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f_L(x):
x = x.flatten()
y1 = (6.0*x-2.0)**2 * np.sin(12.0*x-4.0)
y2 = (6.0*x-2.0)**2 * np.sin(12.0*x-4.0) + 3.0
y = (x<0.5)*y1 + (x>0.5)*y2
return y[0]
def f_H(x):
x = x.flatten()
y1 = 2.0*f_L(x) - 20.0*x + 20.0
y2 = 2.0*f_L(x) - 20.0*x + 20.0 + 4.0
y = (x<0.5)*y1 + (x>0.5)*y2
return y[0]
return (f_L, f_H), p_x, dim, lb, ub
def modified_branin():
dim = 2
lb = np.array([-5.0, 0.0])
ub = np.array([10.0, 15.0])
p_x = uniform_prior(lb, ub)
def f(x):
a = 1.0
b = 5.1 / (4*np.pi**2)
c = 5 / np.pi
r = 6
s = 10
t = 1 / (8*np.pi)
x1, x2 = x[0], x[1]
f1 = a * (x2 - b*x1**2 + c*x1 -r)**2
f2 = s * (1-t) * np.cos(x1) * np.cos(x2)
f3 = np.log(x1**2 + x2**2 + 1)
y = -1/(f1+f2+f3+s)
return y
return f, p_x, dim, lb, ub
def hartmann6():
dim = 6
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f(x):
alpha = np.array([1.0, 1.2, 3.0, 3.2])
A = np.array([[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14]])
P = 1e-4 * np.array([[1312, 1696, 5569, 124, 8283, 5886],
[2329, 4135, 8307, 3736, 1004, 9991],
[2348, 1451, 3522, 2883, 3047, 6650],
[4047, 8828, 8732, 5743, 1091, 381]])
arg = np.dot(A, (x-P).T**2)
y = -np.dot(alpha, np.diag(np.exp(-arg)))
return y
return f, p_x, dim, lb, ub
def singlefidelity_hartmann3():
dim = 3
lb = np.zeros(dim)
ub = np.ones(dim)
p_x = uniform_prior(lb, ub)
def f(x):
alpha = np.array([1.0, 1.2, 3.0, 3.2])
A = np.array([[3, 10, 30],
[0.1, 10, 35],
[3, 10, 30],
[0.1, 10, 35]])
P = 1e-4 * np.array([[3689, 1170, 2673],
[4699, 4387, 7470],
[1091, 8732, 5547],
[381, 5743, 8828]])
arg = np.dot(A, (x-P).T**2)
y = -np.dot(alpha, np.diag(np.exp(-arg)))
return y
return f, p_x, dim, lb, ub
def multifidelity_branin():
dim = 2
lb = np.array([-5.0, 0.0])
ub = np.array([10.0, 15.0])
p_x = uniform_prior(lb, ub)
def f_H(x):
a = 1.0
b = 5.1 / (4*np.pi**2)
c = 5 / np.pi
r = 6
s = 10
t = 1 / (8*np.pi)
x1, x2 = x[0], x[1]
y = a * (x2 - b*x1**2 + c*x1 -r)**2 + s * (1-t) * np.cos(x1) + s
return y
def f_L(x):
y = 0.5*f_H(x) + 10.0*(np.sum(x)-0.5) - 5.0
return y
return (f_L, f_H), p_x, dim, lb, ub
y1_c_star = vmap(constraint1)(X_star)
Y_f_star = griddata(onp.array(X_star), onp.array(y_f_star), (onp.array(XX), onp.array(YY)), method='cubic')
Y1_c_star = griddata(onp.array(X_star), onp.array(y1_c_star), (onp.array(XX), onp.array(YY)), method='cubic')
# Problem settings
# Number of initial data for objective and constraints
N_f = 200
N_c = 200
noise_f = 0.00
noise_c = 0.00
nIter = 1 # 10
# Define prior distribution
p_x = uniform_prior(lb, ub)
# JAX-BO setting
options = {'kernel': 'RBF',
'input_prior': p_x}
layers = [2, 5, 5, 1]
gp_model = ManifoldGP_MultiOutputs(options, layers)
# Domain bounds (already defined before where we visualized the data)
bounds = {'lb': lb, 'ub': ub}
# Initial training data for objective
X_f = lb + (ub-lb)*lhs(dim, N_f)
y_f = vmap(f)(X_f)
y_f = y_f + noise_f*y_f_star.std(0)*onp.random.normal(0, 1, size=y_f.shape)