NSGA2 Python实现

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#importing necessary modules
import math
import random
import matplotlib.pyplot as Plt


#First Function to optimize
def function1(x1,x2):
    value = -x1*2 + x2
    return value
#Second Function to optimize
def function2(x1,x2):

    value = -x1*5*x2
    return value

def index_of(a,list):
    for i in range(0,len(list)):
        if a == list[i]:
            return i
    return 0

#求rank
def cd_index(front,f_values):
    #将front中的目标值排序，
    sorted_index = []
    for i in range(0, len(front)):
        temp_list = []
        temp_index =[]
        for j in front[i]:
            temp_list.append(f_values[j])
        temp_list.sort()
        for n in range(0,len(temp_list)):
            temp_index.append(index_of(temp_list[n],f_values))
        sorted_index.append(temp_index)
    return sorted_index

#求单个目标拥挤度
def crowding_distance(front,f_values):
    #将front中的目标值排序，
    sorted_values = []
    for i in range(0, len(front)):
        temp_list = []
        temp_index =[]
        for j in front[i]:
            temp_list.append(f_values[j])
        temp_list.sort()
        for n in range(0,len(temp_list)):
            temp_index.append(index_of(temp_list[n],f_values))
        sorted_values.append(temp_list)
     #计算拥挤度
    distance = [[] for i in range(0, len(front))]
    for i in range(0, len(front)):
        if len(front[i]) == 1:
            distance[i].append(math.inf)
        elif len(front[i]) == 2:
            distance[i].append(math.inf)
            distance[i].append(math.inf)
        else:
            distance[i].append(math.inf)
            for k in range(1,len(front[i])-1):
                if max(sorted_values[i]) == min(sorted_values[i]):
                    break
                distance[i].append((sorted_values[i][k+1]-sorted_values[i][k-1])/(max(sorted_values[i])-min(sorted_values[i])))
            distance[i].append(math.inf)
    return distance

#求总拥挤度
def Get_TOTAL_Distance(front,f1,f2):
    Tol_Dis = [[] for i in range(0, len(front))]
    tem_tol = []
    crowding_distance1 = crowding_distance(front, f1)  # 每个个体在f1上的拥挤度
    crowding_distance2 = crowding_distance(front, f2)  # 每个个体在f2上的拥挤度
    sorted_index1 = cd_index(front, f1)  # 对f1排序后的个体变换
    sorted_index2 = cd_index(front, f2)  # 对f1排序后的个体变换
    for i in range(0, len(sorted_index1)):
        for j in sorted_index1[i]:
            tem_tol.append(
                crowding_distance1[i][sorted_index1[i].index(j)] + crowding_distance2[i][sorted_index2[i].index(j)])
        Tol_Dis.append(tem_tol)
    return Tol_Dis


def fast_non_dominated_sort(values1,values2):
    S = [[] for i in range(0,len(values1))]
    front = [[]]
    n = [0 for i in range(0,len(values1))]

    for p in range(0,len(values1)):
        #S[p] = []
        #n[p] = 0
        for q in range(0,len(values1)):
            if ( values1[p] < values1[q] and values2[p] < values2[q]) or \
                    (values1[p] < values1[q] and values2[p] <= values2[q]) or \
                    (values1[p] <= values1[q] and values2[p] < values2[q]) :
                S[p].append(q)
            elif ( values1[p] > values1[q] and values2[p] > values2[q]) or \
                    (values1[p] > values1[q] and values2[p] >= values2[q]) or \
                    (values1[p] >= values1[q] and values2[p] > values2[q]) :
                n[p] += 1
        if n[p] == 0:
            front[0].append(p)
    i = 0
    while( front[i] != []):
        Q = []
        for p in front[i]:
            for q in S[p]:
                n[q] -= 1
                if(n[q] == 0):
                    Q.append(q)
        i += 1
        front.append(Q)
    del front[len(front)-1]
    return front

#离散重组
def crossover(a,b):
    r = random.random()
    list = []
    A =[0,0]
    B = [0,0]
    if r>0.5:
        A[0] = mutation(a[0])
        B[1] = mutation(b[1])
        list.append(A[0])
        list.append(B[1])
        return list
    else:
        A[1] = mutation(a[1])
        B[0] = mutation(b[0])
        list.append(B[0])
        list.append(A[1])
        return list

def mutation(a):
    mutation_pro=random.random()
    pop = 0
    if mutation_pro <0.05 :
        pop = min_x[0] + (max_x[0]-min_x[0])*random.random()
        return pop
    elif mutation_pro >0.05 and mutation_pro <0.1 :
        pop = min_x[1] + (max_x[1] - min_x[1]) * random.random()
        return pop
    else:
        return a



#Main program
popsize = 50
max_gen = 200

#Initialization
min_x = [-1,1]
max_x = [2,6]
pop = [[] for i in range(0,popsize)]
for i in range(0,popsize):
    for j in range(0,len(min_x)):
        pop[i].append(min_x[j]+(max_x[j]-min_x[j])*random.random())

gen = 0
while gen<max_gen:
    #Selection
    f1_values = [function1(pop[i][0], pop[i][1]) for i in range(0, popsize)]  # 得到每个个体的目标1值f1
    f2_values = [function2(pop[i][0], pop[i][1]) for i in range(0, popsize)]  # 得到每个个体的目标2值f2
    Front = fast_non_dominated_sort(f1_values[:],f2_values[:])#非支配排序
    #计算拥挤度
    Tol_Dis = Get_TOTAL_Distance(Front,f1_values,f2_values)

    pop2 = pop[:]
    # Generating offsprings
    while (len(pop2)!= 2*popsize) :
        p1 = random.randint(0,popsize-1)
        p2 = random.randint(0, popsize - 1)
        pop2.append(crossover(pop[p1],pop[p2]))

    f1_values1 = [function1(pop2[i][0], pop2[i][1]) for i in range(0, 2*popsize)]  # 得到每个个体的目标1值f1
    f2_values1 = [function2(pop2[i][0], pop2[i][1]) for i in range(0, 2*popsize)]  # 得到每个个体的目标2值f2
    Front1 = fast_non_dominated_sort(f1_values1[:], f2_values1[:])  # 非支配排序
    # 计算拥挤度
    Tol_Dis1 = Get_TOTAL_Distance(Front1, f1_values1, f2_values1)
    #Select
    num = 0
    new_pop_index = []
    for i in range(0, len(Front1)):
        if len(Front1[i]) < (popsize - num):  # 非支配排序选择 popsize是初代种群个数
            for j in range(0,len(Front1[i])):
                new_pop_index.append(Front1[i][j])
        else:  # 拥挤度选择
            for j in range(0, popsize - num):
                new_pop_index.append(Front1[i][j])
                if len(new_pop_index)== popsize:
                    break;
        num += len(Front1[i])
    new_pop = [pop2[i] for i in new_pop_index]
    pop = new_pop
    gen +=1

#plot
function1 = [i * -1  for i in f1_values]
function2 = [j * -1  for j in f2_values]
Plt.xlabel('Function 1 ',fontsize = 15)
Plt.ylabel('Function 2 ',fontsize = 15)
Plt.scatter(function1,function2)
Plt.show()