pymoo包NSGA2算法实现多目标遗传算法调参详细说明

pymoo包NSGA2算法实现多目标遗传算法调参详细说明 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 2.调用NSGA2的算法包设置参数2.1 NSGA2函数的参数设置 3.定义迭代次数90次4.求解最帕累托最优解集的参数x向量4.2 查看输出的X的解 5.帕累托最优解集的X向量参数最优解集分布6.画出帕累托前沿

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 X X变量数量n_obj定义的是待求解 f f 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 X X参数的下限xu定义的是待求解的 X X 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")