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problem.py
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import torch
import numpy as np
def get_problem(name, *args, **kwargs):
name = name.lower()
PROBLEM = {
'f1': F1,
'f2': F2,
'f3': F3,
'f4': F4,
'f5': F5,
'f6': F6,
'vlmop1': VLMOP1,
'vlmop2': VLMOP2,
'vlmop3': VLMOP3,
'dtlz2': DTLZ2,
're21': RE21,
're23': RE23,
're33': RE33,
're36': RE36,
're37': RE37,
}
if name not in PROBLEM:
raise Exception("Problem not found.")
return PROBLEM[name](*args, **kwargs)
class F1():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = sum2 = 0.0
count1 = count2 = 0.0
for i in range(2,n+1):
yi = x[:,i-1] - torch.pow(2 * x[:,0] - 1, 2)
yi = yi * yi
if i % 2 == 0:
sum2 = sum2 + yi
count2 = count2 + 1.0
else:
sum1 = sum1 + yi
count1 = count1 + 1.0
f1 = (1 + 1.0/count1 * sum1 ) * x[:,0]
f2 = (1 + 1.0/count2 * sum2 ) * (1.0 - torch.sqrt(x[:,0] / (1 + 1.0/count2 * sum2 )))
objs = torch.stack([f1,f2]).T
return objs
class F2():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = sum2 = 0.0
count1 = count2 = 0.0
for i in range(2,n+1):
theta = 1.0 + 3.0*(i-2)/(n - 2)
yi = x[:,i-1] - torch.pow(x[:,0], 0.5*theta)
yi = yi * yi
if i % 2 == 0:
sum2 = sum2 + yi
count2 = count2 + 1.0
else:
sum1 = sum1 + yi
count1 = count1 + 1.0
f1 = (1 + 1.0/count1 * sum1 ) * x[:,0]
f2 = (1 + 1.0/count2 * sum2 ) * (1.0 - torch.sqrt(x[:,0] / (1 + 1.0/count2 * sum2 )))
objs = torch.stack([f1,f2]).T
return objs
class F3():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = sum2 = 0.0
count1 = count2 = 0.0
for i in range(2,n+1):
xi = x[:,i-1]
yi = xi - (torch.sin(4.0*np.pi* x[:,0] + i*np.pi/n) + 1) / 2
yi = yi * yi
if i % 2 == 0:
sum2 = sum2 + yi
count2 = count2 + 1.0
else:
sum1 = sum1 + yi
count1 = count1 + 1.0
f1 = (1 + 1.0/count1 * sum1 ) * x[:,0]
f2 = (1 + 1.0/count2 * sum2 ) * (1.0 - torch.sqrt(x[:,0]))
objs = torch.stack([f1,f2]).T
return objs
class F4():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = sum2 = 0
count1 = count2 = 0
for i in range(2,n+1):
xi = -1.0 + 2.0*x[:,i-1]
if i % 2 == 0:
yi = xi - 0.8 * x[:,0] * torch.sin(4.0*np.pi*x[:,0] + i*np.pi/n)
yi = yi * yi
sum2 = sum2 + yi
count2 = count2 + 1.0
else:
yi = xi - 0.8* x[:,0] * torch.cos(4.0*np.pi*x[:,0] + i*np.pi/n)
yi = yi * yi
sum1 = sum1 + yi
count1 = count1 + 1.0
f1 = (1 + 1.0/count1 * sum1 ) * x[:,0]
f2 = (1 + 1.0/count2 * sum2 ) * (1.0 - torch.sqrt(x[:,0] / (1 + 1.0/count2 * sum2 )))
objs = torch.stack([f1,f2]).T
return objs
class F5():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = sum2 = 0
count1 = count2 = 0
for i in range(2,n+1):
xi = -1.0 + 2.0*x[:,i-1]
if i % 2 == 0:
yi = xi - 0.8 * x[:,0] * torch.sin(4.0*np.pi*x[:,0] + i*np.pi/n)
yi = yi * yi
sum2 = sum2 + yi
count2 = count2 + 1.0
else:
yi = xi - 0.8 * x[:,0] * torch.cos((4.0*np.pi*x[:,0] + i*np.pi/n)/3)
yi = yi * yi
sum1 = sum1 + yi
count1 = count1 + 1.0
f1 = (1 + 1.0/count1 * sum1 ) * x[:,0]
f2 = (1 + 1.0/count2 * sum2 ) * (1.0 - torch.sqrt(x[:,0] / (1 + 1.0/count2 * sum2 )))
objs = torch.stack([f1,f2]).T
return objs
class F6():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = sum2 = 0
count1 = count2 = 0
for i in range(2,n+1):
xi = -1.0 + 2.0*x[:,i-1]
if i % 2 == 0:
yi = xi - (0.3 * x[:,0] ** 2 * torch.cos(12.0*np.pi*x[:,0] + 4 *i*np.pi/n) + 0.6 * x[:,0]) * torch.sin(6.0*np.pi*x[:,0] + i*np.pi/n)
yi = yi * yi
yi = yi * yi
sum2 = sum2 + yi
count2 = count2 + 1.0
else:
yi = xi - (0.3 * x[:,0] ** 2 * torch.cos(12.0*np.pi*x[:,0] + 4 *i*np.pi/n) + 0.6 * x[:,0]) * torch.cos(6.0*np.pi*x[:,0] + i*np.pi/n)
yi = yi * yi
sum1 = sum1 + yi
count1 = count1 + 1.0
f1 = (1 + 1.0/count1 * sum1 ) * x[:,0]
f2 = (1 + 1.0/count2 * sum2 ) * (1.0 - torch.sqrt(x[:,0] / (1 + 1.0/count2 * sum2 )))
objs = torch.stack([f1,f2]).T
return objs
class VLMOP1():
def __init__(self, n_dim = 1):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.tensor([-2.0]).float()
self.ubound = torch.tensor([4.0]).float()
self.nadir_point = [4, 4]
def evaluate(self, x):
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
f1 = torch.pow(x[:,0], 2)
f2 = torch.pow(x[:,0] - 2, 2)
objs = torch.stack([f1,f2]).T
return objs
class VLMOP2():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.tensor([-2.0, -2.0, -2.0, -2.0, -2.0, -2.0]).float()
self.ubound = torch.tensor([2.0, 2.0,2.0, 2.0,2.0, 2.0]).float()
self.nadir_point = [1, 1]
def evaluate(self, x):
n = x.shape[1]
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
f1 = 1 - torch.exp(-torch.sum((x - 1 / np.sqrt(n))**2, axis = 1))
f2 = 1 - torch.exp(-torch.sum((x + 1 / np.sqrt(n))**2, axis = 1))
objs = torch.stack([f1,f2]).T
return objs
class VLMOP3():
def __init__(self, n_dim = 2):
self.n_dim = n_dim
self.n_obj = 3
self.lbound = torch.tensor([-3.0, -3.0]).float()
self.ubound = torch.tensor([3.0, 3.0]).float()
self.nadir_point = [10,60,1]
def evaluate(self, x):
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
x1, x2 = x[:, 0], x[:, 1]
f1 = 0.5 * (x1 ** 2 + x2 ** 2) + torch.sin(x1 ** 2 + x2 ** 2)
f2 = (3 * x1 - 2 * x2 + 4) ** 2 / 8 + (x1 - x2 + 1) ** 2 / 27 + 15
f3 = 1 / (x1 ** 2 + x2 ** 2 + 1) - 1.1 * torch.exp(-x1 ** 2 - x2 ** 2)
objs = torch.stack([f1,f2,f3]).T
return objs
class DTLZ2():
def __init__(self, n_dim = 6):
self.n_dim = n_dim
self.n_obj = 3
self.lbound = torch.zeros(n_dim).float()
self.ubound = torch.ones(n_dim).float()
self.nadir_point = [1, 1, 1]
def evaluate(self, x):
n = x.shape[1]
sum1 = torch.sum(torch.stack([torch.pow(x[:,i]-0.5,2) for i in range(2,n)]), axis = 0)
g = sum1
f1 = (1 + g) * torch.cos(x[:,0]*np.pi/2) * torch.cos(x[:,1]*np.pi/2)
f2 = (1 + g) * torch.cos(x[:,0]*np.pi/2) * torch.sin(x[:,1]*np.pi/2)
f3 = (1 + g) * torch.sin(x[:,0]*np.pi/2)
objs = torch.stack([f1,f2, f3]).T
return objs
class RE21():
def __init__(self, n_dim = 4):
F = 10.0
sigma = 10.0
tmp_val = F / sigma
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.tensor([tmp_val, np.sqrt(2.0) * tmp_val, np.sqrt(2.0) * tmp_val, tmp_val]).float()
self.ubound = torch.ones(n_dim).float() * 3 * tmp_val
self.nadir_point = [2886.3695604236013, 0.039999999999998245]
def evaluate(self, x):
F = 10.0
E = 2.0 * 1e5
L = 200.0
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
f1 = L * ((2 * x[:,0]) + np.sqrt(2.0) * x[:,1] + torch.sqrt(x[:,2]) + x[:,3])
f2 = ((F * L) / E) * ((2.0 / x[:,0]) + (2.0 * np.sqrt(2.0) / x[:,1]) - (2.0 * np.sqrt(2.0) / x[:,2]) + (2.0 / x[:,3]))
f1 = f1
f2 = f2
objs = torch.stack([f1,f2]).T
return objs
class RE23():
def __init__(self, n_dim = 4):
self.n_dim = n_dim
self.n_obj = 2
self.lbound = torch.tensor([1, 1, 10,10]).float()
self.ubound = torch.tensor([100, 100, 200, 240]).float()
self.nadir_point = [5852.05896876, 1288669.78054]
def evaluate(self, x):
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
x1 = 0.0625 * torch.round(x[:,0])
x2 = 0.0625 * torch.round(x[:,1])
x3 = x[:,2]
x4 = x[:,3]
#First original objective function
f1 = (0.6224 * x1 * x3* x4) + (1.7781 * x2 * x3 * x3) + (3.1661 * x1 * x1 * x4) + (19.84 * x1 * x1 * x3)
f1 = f1.float()
# Original constraint functions
g1 = x1 - (0.0193 * x3)
g2 = x2 - (0.00954 * x3)
g3 = (np.pi * x3 * x3 * x4) + ((4.0/3.0) * (np.pi * x3 * x3 * x3)) - 1296000
g = torch.stack([g1,g2,g3])
z = torch.zeros(g.shape).cuda().to(torch.float64)
g = torch.where(g < 0, -g, z)
f2 = torch.sum(g, axis = 0).to(torch.float64)
objs = torch.stack([f1,f2]).T
return objs
class RE33():
def __init__(self, n_dim = 4):
self.n_dim = n_dim
self.n_obj = 3
self.lbound = torch.tensor([55, 75, 1000, 11]).float()
self.ubound = torch.tensor([80, 110, 3000, 20]).float()
self.nadir_point = [5.3067, 3.12833430979, 25.0]
def evaluate(self, x):
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
x1 = x[:,0]
x2 = x[:,1]
x3 = x[:,2]
x4 = x[:,3]
# First original objective function
f1 = 4.9 * 1e-5 * (x2 * x2 - x1 * x1) * (x4 - 1.0)
# Second original objective function
f2 = ((9.82 * 1e6) * (x2 * x2 - x1 * x1)) / (x3 * x4 * (x2 * x2 * x2 - x1 * x1 * x1))
# Reformulated objective functions
g1 = (x2 - x1) - 20.0
g2 = 0.4 - (x3 / (3.14 * (x2 * x2 - x1 * x1)))
g3 = 1.0 - (2.22 * 1e-3 * x3 * (x2 * x2 * x2 - x1 * x1 * x1)) / torch.pow((x2 * x2 - x1 * x1), 2)
g4 = (2.66 * 1e-2 * x3 * x4 * (x2 * x2 * x2 - x1 * x1 * x1)) / (x2 * x2 - x1 * x1) - 900.0
g = torch.stack([g1,g2,g3,g4])
z = torch.zeros(g.shape).float().cuda().to(torch.float64)
g = torch.where(g < 0, -g, z)
f3 = torch.sum(g, axis = 0).float()
objs = torch.stack([f1,f2,f3]).T
return objs
class RE36():
def __init__(self, n_dim = 4):
self.n_dim = n_dim
self.n_obj = 3
self.lbound = torch.tensor([12, 12, 12, 12]).float()
self.ubound = torch.tensor([60, 60, 60, 60]).float()
self.nadir_point = [5.931, 56.0, 0.355720675227]
def evaluate(self, x):
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
x1 = x[:,0]
x2 = x[:,1]
x3 = x[:,2]
x4 = x[:,3]
# First original objective function
f1 = torch.abs(6.931 - ((x3 / x1) * (x4 / x2)))
# Second original objective function (the maximum value among the four variables)
l = torch.stack([x1, x2, x3, x4])
f2 = torch.max(l, dim = 0)[0]
g1 = 0.5 - (f1 / 6.931)
g = torch.stack([g1])
z = torch.zeros(g.shape).float().cuda().to(torch.float64)
g = torch.where(g < 0, -g, z)
f3 = g[0]
objs = torch.stack([f1,f2,f3]).T
return objs
class RE37():
def __init__(self, n_dim = 4):
self.n_dim = n_dim
self.n_obj = 3
self.lbound = torch.tensor([0, 0, 0, 0]).float()
self.ubound = torch.tensor([1, 1, 1, 1]).float()
self.nadir_point = [0.98949120096, 0.956587924661, 0.987530948586]
def evaluate(self, x):
if x.device.type == 'cuda':
self.lbound = self.lbound.cuda()
self.ubound = self.ubound.cuda()
x = x * (self.ubound - self.lbound) + self.lbound
xAlpha = x[:,0]
xHA = x[:,1]
xOA = x[:,2]
xOPTT = x[:,3]
# f1 (TF_max)
f1 = 0.692 + (0.477 * xAlpha) - (0.687 * xHA) - (0.080 * xOA) - (0.0650 * xOPTT) - (0.167 * xAlpha * xAlpha) - (0.0129 * xHA * xAlpha) + (0.0796 * xHA * xHA) - (0.0634 * xOA * xAlpha) - (0.0257 * xOA * xHA) + (0.0877 * xOA * xOA) - (0.0521 * xOPTT * xAlpha) + (0.00156 * xOPTT * xHA) + (0.00198 * xOPTT * xOA) + (0.0184 * xOPTT * xOPTT)
# f2 (X_cc)
f2 = 0.153 - (0.322 * xAlpha) + (0.396 * xHA) + (0.424 * xOA) + (0.0226 * xOPTT) + (0.175 * xAlpha * xAlpha) + (0.0185 * xHA * xAlpha) - (0.0701 * xHA * xHA) - (0.251 * xOA * xAlpha) + (0.179 * xOA * xHA) + (0.0150 * xOA * xOA) + (0.0134 * xOPTT * xAlpha) + (0.0296 * xOPTT * xHA) + (0.0752 * xOPTT * xOA) + (0.0192 * xOPTT * xOPTT)
# f3 (TT_max)
f3 = 0.370 - (0.205 * xAlpha) + (0.0307 * xHA) + (0.108 * xOA) + (1.019 * xOPTT) - (0.135 * xAlpha * xAlpha) + (0.0141 * xHA * xAlpha) + (0.0998 * xHA * xHA) + (0.208 * xOA * xAlpha) - (0.0301 * xOA * xHA) - (0.226 * xOA * xOA) + (0.353 * xOPTT * xAlpha) - (0.0497 * xOPTT * xOA) - (0.423 * xOPTT * xOPTT) + (0.202 * xHA * xAlpha * xAlpha) - (0.281 * xOA * xAlpha * xAlpha) - (0.342 * xHA * xHA * xAlpha) - (0.245 * xHA * xHA * xOA) + (0.281 * xOA * xOA * xHA) - (0.184 * xOPTT * xOPTT * xAlpha) - (0.281 * xHA * xAlpha * xOA)
objs = torch.stack([f1,f2,f3]).T
return objs