• 主要是在遺傳符號回歸的代碼中添加了注釋和根據一部分源碼做了一點改動

import operator
import random
import numpy as np
import matplotlib.pyplot as plt
from deap import algorithms, base, creator, tools, gp
from operator import attrgetter##生成數據
def generate_data():X = np.random.uniform(-10, 10, 100).reshape(-1, 1)y = X**3 - 2*X**2 + 3*X - 5 + np.random.normal(0, 5, 100).reshape(-1, 1)return X, y##population:群體
##toolbox:工具箱
##cxpb:交配概率
##mutpb:變異概率
def varAnd(population, toolbox, cxpb, mutpb):offspring = [toolbox.clone(ind) for ind in population]# Apply crossover and mutation on the offspringfor i in range(1, len(offspring), 2):if random.random() < cxpb:offspring[i - 1], offspring[i] = toolbox.mate(offspring[i - 1],offspring[i])del offspring[i - 1].fitness.values, offspring[i].fitness.valuesfor i in range(len(offspring)):if random.random() < mutpb:offspring[i], = toolbox.mutate(offspring[i])del offspring[i].fitness.valuesreturn offspringdef if_then_else(input, output1, output2):return np.where(input, output1, output2)# 定義評價函數
def evalSymbReg(individual, points):func = toolbox.compile(expr=individual)           #編譯表達式sqerrors = ((func(points) - y)**2).flatten()      #誤差計算return np.sqrt(np.sum(sqerrors)),# 挑選好的若干個體
def selTournament(individuals, k, tournsize, fit_attr="fitness"):chosen = []for i in range(k):aspirants = [random.choice(individuals) for i in range(tournsize)]chosen.append(max(aspirants, key=attrgetter(fit_attr)))return chosendef eaSimple2(population, toolbox, cxpb, mutpb, ngen, stats=None,halloffame=None, verbose=__debug__):#用適應度評價群體,對還沒有進行過評價的個體進行評價（主要是存在很多評價過的個體）invalid_ind = []   for ind in population:if not ind.fitness.valid:invalid_ind.append(ind)fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)for ind, fit in zip(invalid_ind, fitnesses):ind.fitness.values = fitif halloffame is not None:    #名人堂halloffame.update(population)#開始迭代過程for gen in range(1, ngen + 1):#1、選擇下一代繁殖個體offspring = toolbox.select(population, len(population))#2、交叉變異offspring = toolbox.varAnd(offspring, toolbox, cxpb, mutpb)#3、對適應度無效的個體進行評價invalid_ind = []for ind in offspring:if not ind.fitness.valid:invalid_ind.append(ind)fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)for ind, fit in zip(invalid_ind, fitnesses):ind.fitness.values = fit#4、更新名人堂if halloffame is not None:halloffame.update(offspring)#5、用后代代替當前的群體population = offspring   #用這種方法可以使用原來的地址return population#################################################################################################
# 1、創建遺傳符號回歸語義集合
pset = gp.PrimitiveSet("MAIN", 1)
pset.addPrimitive(operator.add, 2)
pset.addPrimitive(operator.sub, 2)
pset.addPrimitive(operator.mul, 2)
pset.addPrimitive(operator.neg, 1)
pset.addPrimitive(np.square, 1)
pset.addPrimitive(np.sqrt, 1)
pset.addPrimitive(if_then_else, 3)
pset.addEphemeralConstant("rand101", lambda: random.uniform(-10, 10))# 2、頂級適應度和個體類
creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", gp.PrimitiveTree, fitness=creator.FitnessMin)
# 4、定義工具函數，這里可以引入自定義函數
toolbox = base.Toolbox()
## 4.1 定義個體和種群
toolbox.register("expr", gp.genFull, pset=pset, min_=1, max_=2)                      #在兩個子葉之間生成1-2深度表達式
toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.expr)  #定義個體
toolbox.register("population", tools.initRepeat, list, toolbox.individual)            #生成群體
## 4.2 公式編碼
toolbox.register("compile", gp.compile, pset=pset)                                    #表達式編譯
## 4.3 評價和挑選
X, y = generate_data()
toolbox.register("evaluate", evalSymbReg, points=X)                                #用生成的這些數據進行評價 
toolbox.register("select", selTournament, tournsize=3)                           #個體篩選
## 4.4 交叉變異和下一代繁殖
toolbox.register("mate", gp.cxOnePoint)                                                   #交叉toolbox.register("expr_mut", gp.genFull, min_=0, max_=2)
toolbox.register("mutate", gp.mutUniform, expr=toolbox.expr_mut, pset=pset)               #變異
toolbox.register("select", selTournament, tournsize=3)   toolbox.register("varAnd", varAnd)   #繁殖########################################################################
# 1、定義種群和名人堂
pop = toolbox.population(n=300)        #種群
hof = tools.HallOfFame(10)              #名人堂
# 2、擬合公式
pop = eaSimple2(pop, toolbox, 0.5, 0.1, 40,halloffame=hof, verbose=True)
best_ind = hof[0]
print("擬合公式：",best_ind)
# 3、畫出圖像
func = toolbox.compile(expr=best_ind)
y_pred = func(X)
plt.figure()
plt.scatter(X, y, color='blue', label='Actual data')
plt.scatter(X, y_pred, color='red', label='Predicted data')
plt.legend()
plt.show()