Decomposition¶
Also, multi-objective problems can be decomposed using a scalarization function. In the following, the contour lines of different methods are shown.
Let us first make the necessary imports and define the points in the design space:
[1]:
import matplotlib.pyplot as plt
import numpy as np
from pymoo.factory import get_decomposition
from pymoo.util.misc import all_combinations
# number of points to be used for plotting
n_points = 100
# the xlim
P = np.linspace(0, 3, n_points)
# used for the meshgrid
X = all_combinations(P,P)
A method to plot the contours:
[2]:
def plot_contour(X, F):
_X = X[:, 0].reshape((n_points,n_points))
_Y = X[:, 1].reshape((n_points,n_points))
_Z = F.reshape((n_points,n_points))
fig, ax = plt.subplots()
ax.contour(_X,_Y, _Z, colors='black')
ax.arrow(0, 0, 2.5, 2.5, color='blue', head_width=0.1, head_length=0.1, alpha=0.4)
ax.set_aspect('equal')
And then define the weights to be used by the decomposition functions:
[3]:
weights = [0.5, 0.5]
Achievement Scalarization Function (ASF)¶
Details can be found in [24].
[6]:
plot_contour(X, get_decomposition("asf", eps=0).do(X, weights=weights))
Augmented Achievement Scalarization Function (AASF)¶
Details can be found in [25].
[7]:
plot_contour(X, get_decomposition("aasf", eps=0, beta=5).do(X, weights=weights))
[8]:
plot_contour(X, get_decomposition("aasf", eps=0, beta=25).do(X, weights=weights))
PBI¶
[9]:
plot_contour(X, get_decomposition("pbi", theta=0.5, eps=0).do(X, weights = weights))
[10]:
plot_contour(X, get_decomposition("pbi", theta=1, eps=0).do(X, weights = weights))
[11]:
plot_contour(X, get_decomposition("pbi", theta=5, eps=0).do(X, weights = weights))