RE34.py

import numpy as np
from pymoo.core.problem import ElementwiseProblem
from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.factory import get_sampling, get_crossover, get_mutation
from pymoo.factory import get_termination
from pymoo.optimize import minimize
import matplotlib.pyplot as plt
from pymoo.visualization.pcp import PCP
from pymoo.factory import get_problem, get_reference_directions
from pymoo.visualization.pcp import PCP
from pymoo.visualization.scatter import Scatter
from pymoo.visualization.pcp import PCP
from pymoo.indicators.hv import Hypervolume


class RE34(ElementwiseProblem):
    def __init__(self):
        super().__init__(n_var = 5, n_obj= 3, n_constr= 0 , xl = np.array([1,1,1,1,1]), xu = np.array([3,3,3,3,3]))
    def _evaluate(self, x, out, *args, **kwargs):
        f = np.zeros(3)
        g = np.zeros(0)

        x1 = x[0]
        x2 = x[1]
        x3 = x[2]
        x4 = x[3]
        x5 = x[4]

        f[0] = 1640.2823 + (2.3573285 * x1) + (2.3220035 * x2) + (4.5688768 * x3) + (7.7213633 * x4) + (4.4559504 * x5)
        f[1] = 6.5856 + (1.15 * x1) - (1.0427 * x2) + (0.9738 * x3) + (0.8364 * x4) - (0.3695 * x1 * x4) + (
                0.0861 * x1 * x5) + (0.3628 * x2 * x4) - (0.1106 * x1 * x1) - (0.3437 * x3 * x3) + (
                       0.1764 * x4 * x4)
        f[2] = -0.0551 + (0.0181 * x1) + (0.1024 * x2) + (0.0421 * x3) - (0.0073 * x1 * x2) + (0.024 * x2 * x3) - (
                0.0118 * x2 * x4) - (0.0204 * x3 * x4) - (0.008 * x3 * x5) - (0.0241 * x2 * x2) + (0.0109 * x4 * x4)

        out["F"] = f
        out["G"]= g

problem = RE34()
algorithm = NSGA2(
    pop_size=1200,
    n_offsprings=10,
    sampling=get_sampling("real_random"),
    crossover=get_crossover("real_sbx", prob=0.9, eta=15),
    mutation=get_mutation("real_pm", eta=20),
    eliminate_duplicates=True
)

termination = get_termination("n_gen", 100)
res = minimize(problem,
               algorithm,
               termination,
               seed=1,
               save_history=True,
               verbose=True)

X = res.X #this are the number of variables
F = res.F #this are the number of objectives

plot = Scatter()
plot.add(problem.pareto_front(), plot_type="line", color="black", alpha=0.7)
plot.add(res.F, facecolor="none", edgecolor="green")
plot.show()