from math import cos, pi, sin
from jmetal.core.problem import FloatProblem
from jmetal.core.solution import FloatSolution
"""
.. module:: DTLZ
:platform: Unix, Windows
:synopsis: DTLZ problem family of multi-objective problems.
.. moduleauthor:: Antonio J. Nebro <antonio@lcc.uma.es>
"""
[docs]
class DTLZ1(FloatProblem):
"""Problem DTLZ1. Continuous problem having a flat Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 7 and 3.
"""
def __init__(self, number_of_variables: int = 7, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem."""
super(DTLZ1, self).__init__()
self.obj_directions = [self.MINIMIZE] * number_of_objectives
self.obj_labels = ["$ f_{} $".format(i) for i in range(number_of_objectives)]
self.lower_bound = number_of_variables * [0.0]
self.upper_bound = number_of_variables * [1.0]
[docs]
def number_of_objectives(self) -> int:
return len(self.obj_directions)
[docs]
def number_of_variables(self) -> int:
return len(self.lower_bound)
[docs]
def number_of_constraints(self) -> int:
return 0
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum(
[
(x - 0.5) * (x - 0.5) - cos(20.0 * pi * (x - 0.5))
for x in solution.variables[self.number_of_variables() - k :]
]
)
g = 100 * (k + g)
solution.objectives = [(1.0 + g) * 0.5] * self.number_of_objectives()
for i in range(self.number_of_objectives()):
for j in range(self.number_of_objectives() - (i + 1)):
solution.objectives[i] *= solution.variables[j]
if i != 0:
solution.objectives[i] *= 1 - solution.variables[self.number_of_objectives() - (i + 1)]
return solution
[docs]
def name(self):
return "DTLZ1"
[docs]
class DTLZ2(DTLZ1):
"""Problem DTLZ2. Continuous problem having a convex Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 12 and 3.
"""
def __init__(self, number_of_variables: int = 12, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem"""
super(DTLZ2, self).__init__(number_of_variables, number_of_objectives)
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum([(x - 0.5) * (x - 0.5) for x in solution.variables[self.number_of_variables() - k :]])
solution.objectives = [1.0 + g] * self.number_of_objectives()
for i in range(self.number_of_objectives()):
for j in range(self.number_of_objectives() - (i + 1)):
solution.objectives[i] *= cos(solution.variables[j] * 0.5 * pi)
if i != 0:
solution.objectives[i] *= sin(0.5 * pi * solution.variables[self.number_of_objectives() - (i + 1)])
return solution
[docs]
def name(self):
return "DTLZ2"
[docs]
class DTLZ3(DTLZ1):
"""Problem DTLZ3. Continuous problem having a convex Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 12 and 3.
"""
def __init__(self, number_of_variables: int = 12, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem"""
super(DTLZ3, self).__init__(number_of_variables, number_of_objectives)
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum(
[(x - 0.5) ** 2 - cos(20.0 * pi * (x - 0.5)) for x in solution.variables[self.number_of_variables() - k :]]
)
g = 100.0 * (k + g)
f = [1.0 + g for _ in range(self.number_of_objectives())]
for i in range(self.number_of_objectives()):
for j in range(self.number_of_objectives() - (i + 1)):
f[i] *= cos(solution.variables[j] * 0.5 * pi)
if i != 0:
aux = self.number_of_objectives() - (i + 1)
f[i] *= sin(solution.variables[aux] * 0.5 * pi)
solution.objectives = [f[x] for x in range(self.number_of_objectives())]
return solution
[docs]
def name(self):
return "DTLZ3"
[docs]
class DTLZ4(DTLZ1):
"""Problem DTLZ4. Continuous problem having a convex Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 12 and 3.
"""
def __init__(self, number_of_variables: int = 12, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem"""
super(DTLZ4, self).__init__(number_of_variables, number_of_objectives)
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
alpha = 100.0
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum([(x - 0.5) ** 2 for x in solution.variables[self.number_of_variables() - k :]])
f = [1.0 + g for _ in range(self.number_of_objectives())]
for i in range(self.number_of_objectives()):
for j in range(self.number_of_objectives() - (i + 1)):
f[i] *= cos(pow(solution.variables[j], alpha) * pi / 2.0)
if i != 0:
aux = self.number_of_objectives() - (i + 1)
f[i] *= sin(pow(solution.variables[aux], alpha) * pi / 2.0)
solution.objectives = [f[x] for x in range(self.number_of_objectives())]
return solution
[docs]
def name(self):
return "DTLZ4"
[docs]
class DTLZ5(DTLZ1):
"""Problem DTLZ5. Continuous problem having a convex Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 12 and 3.
"""
def __init__(self, number_of_variables: int = 12, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem"""
super(DTLZ5, self).__init__(number_of_variables, number_of_objectives)
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum([(x - 0.5) ** 2 for x in solution.variables[self.number_of_variables() - k :]])
t = pi / (4.0 * (1.0 + g))
theta = [0.0] * (self.number_of_objectives() - 1)
theta[0] = solution.variables[0] * pi / 2.0
theta[1:] = [t * (1.0 + 2.0 * g * solution.variables[i]) for i in range(1, self.number_of_objectives() - 1)]
f = [1.0 + g for _ in range(self.number_of_objectives())]
for i in range(self.number_of_objectives()):
for j in range(self.number_of_objectives() - (i + 1)):
f[i] *= cos(theta[j])
if i != 0:
aux = self.number_of_objectives() - (i + 1)
f[i] *= sin(theta[aux])
solution.objectives = [f[x] for x in range(self.number_of_objectives())]
return solution
[docs]
def name(self):
return "DTLZ5"
[docs]
class DTLZ6(DTLZ1):
"""Problem DTLZ6. Continuous problem having a convex Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 12 and 3.
"""
def __init__(self, number_of_variables: int = 12, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem"""
super(DTLZ6, self).__init__(number_of_variables, number_of_objectives)
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum([pow(x, 0.1) for x in solution.variables[self.number_of_variables() - k :]])
t = pi / (4.0 * (1.0 + g))
theta = [0.0] * (self.number_of_objectives() - 1)
theta[0] = solution.variables[0] * pi / 2.0
theta[1:] = [t * (1.0 + 2.0 * g * solution.variables[i]) for i in range(1, self.number_of_objectives() - 1)]
f = [1.0 + g for _ in range(self.number_of_objectives())]
for i in range(self.number_of_objectives()):
for j in range(self.number_of_objectives() - (i + 1)):
f[i] *= cos(theta[j])
if i != 0:
aux = self.number_of_objectives() - (i + 1)
f[i] *= sin(theta[aux])
solution.objectives = [f[x] for x in range(self.number_of_objectives())]
return solution
[docs]
def name(self):
return "DTLZ6"
[docs]
class DTLZ7(DTLZ1):
"""Problem DTLZ6. Continuous problem having a disconnected Pareto front
.. note:: Unconstrained problem. The default number of variables and objectives are, respectively, 22 and 3.
"""
def __init__(self, number_of_variables: int = 22, number_of_objectives=3):
""":param number_of_variables: number of decision variables of the problem"""
super(DTLZ7, self).__init__(number_of_variables, number_of_objectives)
[docs]
def evaluate(self, solution: FloatSolution) -> FloatSolution:
k = self.number_of_variables() - self.number_of_objectives() + 1
g = sum([x for x in solution.variables[self.number_of_variables() - k :]])
g = 1.0 + (9.0 * g) / k
h = sum(
[(x / (1.0 + g)) * (1 + sin(3.0 * pi * x)) for x in solution.variables[: self.number_of_objectives() - 1]]
)
h = self.number_of_objectives() - h
solution.objectives[: self.number_of_objectives() - 1] = solution.variables[: self.number_of_objectives() - 1]
solution.objectives[-1] = (1.0 + g) * h
return solution
[docs]
def name(self):
return "DTLZ7"
