import math
from abc import ABCMeta
from jmetal.core.problem import FloatProblem
from jmetal.core.solution import FloatSolution
"""
.. module:: LZ09
:platform: Unix, Windows
:synopsis: LZ09 problem family of multi-objective problems.
.. moduleauthor:: Antonio Benítez-Hidalgo <antonio.b@uma.es>
"""
[docs]
class LZ09(FloatProblem):
__metaclass__ = ABCMeta
def __init__(
self,
number_of_variables: int,
ptype: int,
dtype: int,
ltype: int,
):
"""LZ09 benchmark family as defined in:
* H. Li and Q. Zhang. Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II.
IEEE Transactions on Evolutionary Computation, 12(2):284-302, April 2009.
"""
super(LZ09, self).__init__()
self.lower_bound = number_of_variables * [0.0]
self.upper_bound = number_of_variables * [1.0]
self.ptype = ptype
self.dtype = dtype
self.ltype = ltype
[docs]
def number_of_constraints(self) -> int:
return 0
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
x = solution.variables
y = self.objective(x)
for i in range(self.number_of_objectives()):
solution.objectives[i] = y[i]
return solution
def __ps_func2(self, x: float, t1: float, dim: int, type: int, css: int) -> float:
"""Control the PS shapes of 2-D instances.
:param type: The type of the curve.
:param css: The class of the index.
"""
beta = 0.0
dim += 1
if type == 21:
xy = 2 * (x - 0.5)
beta = xy - math.pow(t1, 0.5 * (self.number_of_variables() + 3 * dim - 8) / (self.number_of_variables() - 2))
if type == 22:
theta = 6 * math.pi * t1 + dim * math.pi / self.number_of_variables()
xy = 2 * (x - 0.5)
beta = xy - math.sin(theta)
if type == 23:
theta = 6 * math.pi * t1 + dim * math.pi / self.number_of_variables()
ra = 0.8 * t1
xy = 2 * (x - 0.5)
if css == 1:
beta = xy - ra * math.cos(theta)
else:
beta = xy - ra * math.sin(theta)
if type == 24:
theta = 6 * math.pi * t1 + dim * math.pi / self.number_of_variables()
xy = 2 * (x - 0.5)
ra = 0.8 * t1
if css == 1:
beta = xy - ra * math.cos(theta / 3)
else:
beta = xy - ra * math.sin(theta)
if type == 25:
rho = 0.8
phi = math.pi * t1
theta = 6 * math.pi * t1 + dim * math.pi / self.number_of_variables()
xy = 2 * (x - 0.5)
if css == 1:
beta = xy - rho * math.sin(phi) * math.sin(theta)
elif css == 2:
beta = xy - rho * math.sin(phi) * math.cos(theta)
else:
beta = xy - rho * math.cos(phi)
if type == 26:
theta = 6 * math.pi * t1 + dim * math.pi / self.number_of_variables()
ra = 0.3 * t1 * (t1 * math.cos(4 * theta) + 2)
xy = 2 * (x - 0.5)
if css == 1:
beta = xy - ra * math.cos(theta)
else:
beta = xy - ra * math.sin(theta)
return beta
def __ps_func3(self, x: float, t1: float, t2: float, dim: int, type: int):
"""Control the PS shapes of 3-D instances.
:param type: The type of curve.
"""
beta = 0.0
dim += 1
if type == 31:
xy = 4 * (x - 0.5)
rate = 1.0 * dim / self.number_of_variables()
beta = xy - 4 * (t1 * t1 * rate + t2 * (1.0 - rate)) + 2
if type == 32:
theta = 2 * math.pi * t1 + dim * math.pi / self.number_of_variables()
xy = 4 * (x - 0.5)
beta = xy - 2 * t2 * math.sin(theta)
return beta
def __alpha_func(self, x: list, dim: int, type: int) -> list:
"""Control the PF shape."""
alpha = [0.0] * dim
if dim == 2:
if type == 21:
alpha[0] = x[0]
alpha[1] = 1 - math.sqrt(x[0])
if type == 22:
alpha[0] = x[0]
alpha[1] = 1 - x[0] * x[0]
if type == 23:
alpha[0] = x[0]
alpha[1] = 1 - math.sqrt(alpha[0]) - alpha[0] * math.sin(10 * alpha[0] * alpha[0] * math.pi)
if type == 24:
alpha[0] = x[0]
alpha[1] = 1 - x[0] - 0.05 * math.sin(4 * math.pi * x[0])
else:
if type == 31:
alpha[0] = math.cos(x[0] * math.pi / 2) * math.cos(x[1] * math.pi / 2)
alpha[1] = math.cos(x[0] * math.pi / 2) * math.sin(x[1] * math.pi / 2)
alpha[2] = math.sin(x[0] * math.pi / 2)
if type == 32:
alpha[0] = 1 - math.cos(x[0] * math.pi / 2) * math.cos(x[1] * math.pi / 2)
alpha[1] = 1 - math.cos(x[0] * math.pi / 2) * math.sin(x[1] * math.pi / 2)
alpha[2] = 1 - math.sin(x[0] * math.pi / 2)
if type == 33:
alpha[0] = x[0]
alpha[1] = x[1]
alpha[2] = 3 - (math.sin(3 * math.pi * x[0]) + math.sin(3 * math.pi * x[1]) - 2 * (x[0] + x[1]))
if type == 34:
alpha[0] = x[0] - x[1]
alpha[1] = x[0] * (1 - x[1])
alpha[2] = 1 - x[0]
return alpha
def __beta_func(self, x: list, type: int) -> float:
"""Control the distance."""
beta = 0.0
dim = len(x)
if dim == 0:
beta = 0.0
if type == 1:
for i in range(dim):
beta += x[i] * x[i]
beta = 2.0 * beta / dim
if type == 2:
for i in range(dim):
beta += math.sqrt(i + 1) * x[i] * x[i]
beta = 2.0 * beta / dim
if type == 3:
sum, xx = 0, 0
for i in range(dim):
xx = 2 * x[i]
sum += xx * xx - math.cos(4 * math.pi * xx) + 1
beta = 2.0 * sum / dim
if type == 4:
sum, prod, xx = 0, 1, 0
for i in range(dim):
xx = 2 * x[i]
sum += xx * xx
prod *= math.cos(10 * math.pi * xx / math.sqrt(i + 1))
beta = 2.0 * (sum - 2 * prod + 2) / dim
return beta
[docs]
def objective(self, x_variables: list) -> list:
aa = []
bb = []
cc = []
y_objectives = [0.0] * self.number_of_objectives()
if self.number_of_objectives() == 2:
if self.ltype in [21, 22, 23, 24, 26]:
for n in range(1, self.number_of_variables()):
if n % 2 == 0:
a = self.__ps_func2(x_variables[n], x_variables[0], n, self.ltype, 1)
aa.append(a)
else:
b = self.__ps_func2(x_variables[n], x_variables[0], n, self.ltype, 2)
bb.append(b)
g = self.__beta_func(aa, self.dtype)
h = self.__beta_func(bb, self.dtype)
alpha = self.__alpha_func(x_variables, 2, self.ptype)
y_objectives[0] = alpha[0] + h
y_objectives[1] = alpha[1] + g
if self.ltype == 25:
for n in range(1, self.number_of_variables()):
if n % 3 == 0:
a = self.__ps_func2(x_variables[n], x_variables[0], n, self.ltype, 1)
aa.append(a)
elif n % 3 == 1:
b = self.__ps_func2(x_variables[n], x_variables[n], n, self.ltype, 2)
bb.append(b)
else:
c = self.__ps_func2(x_variables[n], x_variables[0], n, self.ltype, 3)
if n % 2 == 0:
aa.append(c)
else:
bb.append(c)
g = self.__beta_func(aa, self.dtype)
h = self.__beta_func(bb, self.dtype)
alpha = self.__alpha_func(x_variables, 2, self.ptype)
y_objectives[0] = alpha[0] + h
y_objectives[1] = alpha[1] + g
if self.number_of_objectives() == 3:
if self.ltype == 31 or self.ltype == 32:
for n in range(2, self.number_of_variables()):
a = self.__ps_func3(x_variables[n], x_variables[0], x_variables[1], n, self.ltype)
if n % 3 == 0:
aa.append(a)
elif n % 3 == 1:
bb.append(a)
else:
cc.append(a)
g = self.__beta_func(aa, self.dtype)
h = self.__beta_func(bb, self.dtype)
e = self.__beta_func(cc, self.dtype)
alpha = self.__alpha_func(x_variables, 3, self.ptype)
y_objectives[0] = alpha[0] + h
y_objectives[1] = alpha[1] + g
y_objectives[2] = alpha[2] + e
return y_objectives
[docs]
def get_name(self):
return "LZ09"
[docs]
class LZ09_F1(LZ09):
def __init__(self, number_of_variables=10):
super(LZ09_F1, self).__init__(
number_of_variables, dtype=1, ltype=21, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F1"
[docs]
class LZ09_F2(LZ09):
def __init__(self, number_of_variables=30):
super(LZ09_F2, self).__init__(
number_of_variables, dtype=1, ltype=22, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F2"
[docs]
class LZ09_F3(LZ09):
def __init__(self, number_of_variables=30):
super(LZ09_F3, self).__init__(
number_of_variables, dtype=1, ltype=23, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F3"
[docs]
class LZ09_F4(LZ09):
def __init__(self, number_of_variables=30):
super(LZ09_F4, self).__init__(
number_of_variables, dtype=1, ltype=24, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F4"
[docs]
class LZ09_F5(LZ09):
def __init__(self, number_of_variables=30):
super(LZ09_F5, self).__init__(
number_of_variables, dtype=1, ltype=26, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F5"
[docs]
class LZ09_F6(LZ09):
def __init__(self, number_of_variables=10):
super(LZ09_F6, self).__init__(
number_of_variables, dtype=1, ltype=32, ptype=31
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)", "f(z)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F6"
[docs]
class LZ09_F7(LZ09):
def __init__(self, number_of_variables=10):
super(LZ09_F7, self).__init__(
number_of_variables, dtype=3, ltype=21, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F7"
[docs]
class LZ09_F8(LZ09):
def __init__(self, number_of_variables=10):
super(LZ09_F8, self).__init__(
number_of_variables, dtype=4, ltype=21, ptype=21
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F8"
[docs]
class LZ09_F9(LZ09):
def __init__(self, number_of_variables=30):
super(LZ09_F9, self).__init__(
number_of_variables, dtype=1, ltype=22, ptype=22
)
self.obj_directions = [self.MINIMIZE, self.MINIMIZE]
self.obj_labels = ["f(x)", "f(y)"]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def name(self):
return "LZ09_F9"
