def CylinderProblem():
"""Return a simple cylinder ScalarMOProblem.
Note:
In this problem consider a cell shaped like a cylinder with a circular
cross-section.
The shape of the cell is here determined by two quantities, its radius
`r` and its height `h`. We want to maximize the volume of the cylinder
and minimize the surface area. In addition to this, cylinder's height
should be close to 15 units, i.e. we minimize the absolute difference
between the height and 15.
Finally the cylinder's height must be greater or equal to its
width. Thus there are 2 decision variables, 3 objectives and 1
constraint in this problem.
"""
# Variables r := x[0], h := x[1]
variables = []
variables.append(Variable("radius", 10, 5, 15))
variables.append(Variable("height", 10, 5, 25))
# Objectives
objectives = []
objectives.append(
ScalarObjective("Volume", lambda x: np.pi * x[0] ** 2 * x[1])
)
objectives.append(
ScalarObjective(
"Surface area",
lambda x: -(2 * np.pi * x[0] ** 2 + 2 * np.pi * x[0] * x[1]),
)
)
objectives.append(
ScalarObjective("Height Difference", lambda x: abs(x[1] - 15.0))
)
# Constraints
constraints = []
constraints.append(
ScalarConstraint(
"Height greater than width",
len(variables),
len(objectives),
constraint_function_factory(
lambda x, f: 2 * x[0] - x[1], 0.0, "<"
),
)
)
# problem
problem = ScalarMOProblem(objectives, variables, constraints)
return problem
def scalar_objectives():
def fun1(d_vars):
return d_vars[0] + d_vars[1] + d_vars[2]
def fun2(d_vars):
return d_vars[3] - d_vars[1] * d_vars[2]
def fun3(d_vars):
return d_vars[2]
obj_1 = ScalarObjective("f1", fun1)
obj_2 = ScalarObjective("f2", fun2)
obj_3 = ScalarObjective("f3", fun3)
return [obj_1, obj_2, obj_3]
def RiverPollutionProblem():
"""Return the river pollution problem as defined in `Miettinen 2010`_
.. _Miettinen 2010:
Miettinen, K.; Eskelinen, P.; Ruiz, F. & Luque, M.
NAUTILUS method: An interactive technique in multiobjective
optimization based on the nadir point
Europen Joural of Operational Research, 2010, 206, 426-434
"""
# Variables
variables = []
variables.append(Variable("x_1", 0.5, 0.3, 1.0))
variables.append(Variable("x_2", 0.5, 0.3, 1.0))
# Objectives
objectives = []
objectives.append(ScalarObjective("f_1", lambda x: -4.07 - 2.27 * x[0]))
objectives.append(
ScalarObjective(
"f_2",
lambda x: -2.60
- 0.03 * x[0]
- 0.02 * x[1]
- 0.01 / (1.39 - x[0] ** 2)
- 0.30 / (1.39 - x[1] ** 2),
)
)
objectives.append(
ScalarObjective("f_3", lambda x: -8.21 + 0.71 / (1.09 - x[0] ** 2))
)
objectives.append(
ScalarObjective("f_4", lambda x: -0.96 + 0.96 / (1.09 - x[1] ** 2))
)
# problem
problem = ScalarMOProblem(objectives, variables, [])
return problem
def DTLZ1_3D():
n = 3
variables = []
for i in range(n):
variables.append(Variable("x{}".format(i), 0.5, 0, 1))
def g(x):
return 100 * (n - 2) + 100 * (
np.sum((x[2:] - 0.5) ** 2 - np.cos(20 * np.pi * (x[2:] - 0.5)))
)
objectives = []
objectives.append(
ScalarObjective("f1", lambda x: (1 + g(x)) * x[0] * x[1])
)
objectives.append(
ScalarObjective("f2", lambda x: (1 + g(x)) * x[0] * (1 - x[1]))
)
objectives.append(ScalarObjective("f3", lambda x: (1 + g(x)) * (1 - x[0])))
constraints = []
for i in range(n):
constraints.append(
ScalarConstraint(
"",
len(variables),
len(objectives),
constraint_function_factory(lambda x, f: x[i], 0.0, ">"),
)
)
constraints.append(
ScalarConstraint(
"",
len(variables),
len(objectives),
constraint_function_factory(lambda x, f: x[i], 1.0, "<"),
)
)
problem = ScalarMOProblem(objectives, variables, constraints)
return problem
def scalar_obj_1():
def fun(vec):
return vec[0] + vec[1] + vec[2]
return ScalarObjective("Objective 1", fun, -10, 10)
def test_bad_bounds():
with pytest.raises(ObjectiveError):
ScalarObjective("", None, -10.0, -11.0)
def test_default_bounds():
obj = ScalarObjective("", None)
assert obj.lower_bound == -np.inf
assert obj.upper_bound == np.inf