Disclaimer: I am the main developer of pymoo, a multi-objective optimization framework in Python.
You might want to consider other frameworks in Python that have a focus on multi-objective optimization. For instance, in pymoo the definition of the rather simple test problem mentioned above is more or less straightforward. You can find an implementation of it below. The results in the design and objectives space look as follows:
pymoo is well documented and provides a getting started guide that demonstrates defining your own optimization problem, obtaining a set of near-optimal solutions and analyzing it: https://pymoo.org/getting_started.html
The focus of the framework is anything related to multi-objective optimization including visualization and decision making.
import matplotlib.pyplot as plt
import numpy as np
from pymoo.algorithms.nsga2 import NSGA2
from pymoo.model.problem import Problem
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter
class MyProblem(Problem):
def __init__(self):
"""
max f1 = X1 <br>
max f2 = 3 X1 + 4 X2 <br>
st X1 <= 20 <br>
X2 <= 40 <br>
5 X1 + 4 X2 <= 200 <br>
"""
super().__init__(n_var=2,
n_obj=2,
n_constr=1,
xl=np.array([0, 0]),
xu=np.array([20, 40]))
def _evaluate(self, x, out, *args, **kwargs):
# define both objectives
f1 = x[:, 0]
f2 = 3 * x[:, 0] + 4 * x[:, 1]
# we have to negate the objectives because by default we assume minimization
f1, f2 = -f1, -f2
# define the constraint as a less or equal to zero constraint
g1 = 5 * x[:, 0] + 4 * x[:, 1] - 200
out["F"] = np.column_stack([f1, f2])
out["G"] = g1
problem = MyProblem()
algorithm = NSGA2()
res = minimize(problem,
algorithm,
('n_gen', 200),
seed=1,
verbose=True)
print(res.X)
print(res.F)
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))
Scatter(fig=fig, ax=ax1, title="Design Space").add(res.X, color="blue").do()
Scatter(fig=fig, ax=ax2, title="Objective Space").add(res.F, color="red").do()
plt.show()
