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()