1.定义待求解问题

1.0定义问题的参数说明

• 1.0.0 求解问题必须设置在def _evaluate(self, x, out, *args, **kwargs)函数中

• 1.0.1 问题必须用 out[“F”] = [f1, f2] 包裹起来

• 1.0.2 约束条件也必须用 out[“G”] = [g3] 包裹起来

• 1.0.3 def __init__(self):里需要定义以下参数

• n_var定义的是待求解的 $X$变量数量
• n_obj定义的是待求解 $f$ 问题数量
• n_ieq_constr定义的是约束条件的数量
• xl定义的是待求解的$X$参数的下限
• xu定义的是待求解的$X$参数的上限
• f1,f2定义问题
• g1,g2定义约束条件

• 1.0.4 约束条件的g以不等式形式写明 会按照小于等于0 进行选择

import numpy as np
from pymoo.core.problem import ElementwiseProblem

class MyProblem(ElementwiseProblem):

    def __init__(self):
        super().__init__(n_var=2, # X 变量数量
                         n_obj=2, # f 问题数
                         n_ieq_constr=1,# g 约束条件数量
                         xl=np.array([-2,-2]), # X 自变量下限
                         xu=np.array([2,2])# X 自变量上限
                         ) 

    def _evaluate(self, x, out, *args, **kwargs):
        # 待求解函数 
        f1 = np.cos(x[0]+x[1]) #100 * (x[0]**2 + x[1]**2) 
        f2 = np.sin(x[0]+x[1]) #(x[0]-1)**2 + x[1]**2
        # f3 = (abs(x[0])<0.3)+(abs(x[1])<0.5)

        # 约束条件会选择 <= 0 的选择
        # g1 = 2*(x[0]-0.1) * (x[0]-0.9) / 0.18
        # g2 = - 20*(x[0]-0.4) * (x[0]-0.6) / 4.8
        # g3 = ((x[0]**2)<0.5)+((x[1]**2)>0.3)
        g3 = x[0]-0.7 #+(abs(x[1])<0.3)

        out["F"] = [f1, f2] #待求解问题
        #out["G"] = [g1, g2,g3] #约束条件
        out["G"] = [g3] #约束条件


problem = MyProblem()

2.调用NSGA2的算法包设置参数

2.1 NSGA2函数的参数设置

• pop_sizez种群数量
• n_offsprings每代的数量
• sampling#抽样设置
• crossove()交叉配对设置
• • prob交叉配对的概率设置
• • eta
• mutation()变异译概率
• • prob是变异的概率设置
• • eta
• eliminate_duplicates我们启用重复检查（“eliminate_duplicates=True”），确保交配产生的后代在设计空间值方面与自身和现有种群不同。

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.operators.crossover.sbx import SBX
from pymoo.operators.mutation.pm import PM
from pymoo.operators.sampling.rnd import FloatRandomSampling,IntegerRandomSampling,BinaryRandomSampling

algorithm = NSGA2(
   pop_size=90, # z种群数量
   n_offsprings=100, # 每代的数量
   sampling= FloatRandomSampling(), #抽样设置
    #交叉配对
   crossover=SBX(prob=0.9 #交叉配对概率
                 , eta=15), #配对效率
   #变异
   mutation=PM(prob=0.8 #编译概率
               ,eta=20),# 配对效率
   eliminate_duplicates=True
)

3.定义迭代次数90次

from pymoo.termination import get_termination

termination = get_termination("n_gen", 90)

4.求解最帕累托最优解集的参数x向量

from pymoo.optimize import minimize

res = minimize(problem,
               algorithm,
               termination,
               seed=1,
               save_history=True,
               verbose=True)

X = res.X # 求解出来的参数
F = res.F # 帕累托最优解集

4.2 查看输出的X的解

array([[-1.22983903, -0.3408983 ],
       [-1.17312926, -1.9683635 ],
       [-1.62815244, -1.25867184],
       [-1.59459202, -1.24720921],
       [-0.85812605, -0.86104326],
       [ 0.14217774, -1.79408273],
       [-1.16038493, -0.45298884],
       [-1.30857014, -0.53215836],
       [-0.99480251, -1.0484723 ],
       [-1.17506923, -0.83512127],
       [-1.12330204, -1.13340585],
       [-1.02395611, -1.33764674],
       [-0.99658648, -0.88776711],
       [-0.87963539, -0.86581268],
       [-1.59330301, -0.09593218],
       [-1.89860429, -1.07240541],
       [-0.92025241, -0.88515559],
       [-1.89221588, -1.02590525],
       [-1.15977198, -0.61984559],
       [-1.23391136, -1.89214062],
       [-1.08575639, -1.1960931 ],
       [-1.8422881 , -1.17730121],
       [-1.97907088, -0.67847822],
       [-1.19339619, -1.30837703],
       [-1.81657534, -0.6468284 ],
       [-1.34872892, -1.1691978 ],
       [-1.70461135, -1.08101794],
       [-1.28766298, -0.92085304],
       [-1.10488217, -1.16702018],
       [-1.45199598, -0.92807938],
       [-1.83785271, -0.26933177],
       [-1.10292853, -1.0760453 ],
       [-1.97460715, -1.02344251],
       [-1.92346673, -1.17730121],
       [-1.35716933, -0.9513154 ],
       [-1.07370789, -1.16339584],
       [-1.61844778, -0.54832033],
       [-1.69262569, -1.29666833],
       [-1.1205858 , -1.9683635 ],
       [-1.32886108, -1.09105746],
       [-0.87963539, -0.85896725],
       [-1.17319829, -1.50153054],
       [-1.63954555, -1.28599005],
       [-0.92662448, -0.93538073],
       [-1.29072744, -0.82715754],
       [-1.72496415, -1.22313643],
       [-1.70410919, -1.36171497],
       [-1.57300848, -1.04123091],
       [-1.81522276, -0.66364657],
       [-1.28643454, -1.14856238],
       [-1.13870379, -0.8286136 ],
       [-1.60254074, -1.21320856],
       [-1.3972806 , -0.68146238],
       [-1.37242908, -0.92807938],
       [-1.29950364, -0.37689045],
       [-1.32237812, -1.09105746],
       [-1.59549137, -1.35399596],
       [-0.86920703, -1.22313643],
       [-1.38180886, -1.34157915],
       [-1.46024398, -1.24232167],
       [-1.12485534, -1.47579521],
       [-1.24917941, -1.2408934 ],
       [-1.6174287 , -1.02798238],
       [-1.46214609, -0.68146238],
       [-0.89315598, -0.95504252],
       [-1.2693953 , -1.07649403],
       [-1.31640451, -1.32237493],
       [-1.2414329 , -1.15952844],
       [-1.10828403, -0.80474544],
       [-1.06864911, -0.83165391],
       [-1.83785271, -1.1960931 ],
       [-1.03382957, -1.50125804],
       [-1.81678927, -0.71106355],
       [-1.12485534, -1.50226124],
       [-1.14170746, -1.05251568],
       [-0.37583973, -1.94856256],
       [-1.19888652, -0.86892885],
       [-1.44462396, -0.94172587],
       [-1.57293402, -1.19861388],
       [-1.7873066 , -1.04123091],
       [-1.19339619, -0.74337764],
       [-1.41439116, -0.77744839],
       [-1.03394747, -1.65557748],
       [-1.29621172, -0.30606688],
       [-0.85812605, -1.09549174],
       [-1.31640451, -1.39906326],
       [-1.36337969, -1.03256822],
       [-1.59459202, -1.20585082],
       [-1.10292853, -1.02523266],
       [-1.85491578, -0.88327578]])

5.帕累托最优解集的X向量参数最优解集分布

import matplotlib.pyplot as plt 
plt.figure(figsize=(16,16))
plt.scatter(X[:,0],X[:,-1])

6.画出帕累托前沿

import matplotlib.pyplot as plt 
plt.figure(figsize=(16,9))
plt.scatter(F[:,0],F[:,-1])
plt.savefig("NSGA2demo帕累托前沿.png")