RE21.py

#this code mainly focuses on exploring the NSGA2 and this code was part of the research work on how to define the problems for the NSGA2 
#to be used via Pymoo. This structure is used in all the workable code for neural networks to be built and train.

import numpy as np
from pymoo.core.problem import ElementwiseProblem
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 RE21(ElementwiseProblem):
    def __init__(selfself):
        super().__init__(n_var =4, n_obj = 2, n_constr = 0 ,xl = np.array([1,1.4142135,1.41421356,1]), xu = np.array([3,3,3,3]))

    def _evaluate(self, x, out, *Args, **kwargs):
        f = np.zeros(2)
        x1 = x[0]
        x2 = x[1]
        x3 = x[2]
        x4 = x[3]

        F = 10.0
        sigma = 10.0
        E = 2.0 * 1e5
        L = 200.0

        f[0] = L * ((2 * x1) + np.sqrt(2.0) * x2 + np.sqrt(x3) + x4)
        f[1] = ((F * L) / E) * ((2.0 / x1) + (2.0 * np.sqrt(2.0) / x2) - (2.0 * np.sqrt(2.0) / x3) + (2.0 / x4))
        out["F"] = f


problem = RE21()
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.show()