NSGA２算法原理及python实现

git参考代码

# Program Name: NSGA-II.py
# Description: This is a python implementation of Prof. Kalyanmoy Deb's popular NSGA-II algorithm
# Author: Haris Ali Khan
# Supervisor: Prof. Manoj Kumar Tiwari
"""
优化目标：min（f1(x), f2(x))f1(x) = -x^2f2(X) = -(x-2)^2s.t x~[-55, 55]
pop_size = 20
max_gen  =  921"""
#Importing required modules
import math
import random
import matplotlib.pyplot as plt#First function to optimize
def function1(x):value = -x**2return value#Second function to optimize
def function2(x):value = -(x-2)**2return value#Function to find index of list
def index_of(a,list):for i in range(0,len(list)):if list[i] == a:return ireturn -1#Function to sort by values
def sort_by_values(list1, values):sorted_list = []while(len(sorted_list)!=len(list1)):if index_of(min(values),values) in list1:sorted_list.append(index_of(min(values),values))values[index_of(min(values),values)] = math.infreturn sorted_list#Function to carry out NSGA-II's fast non dominated sort
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))]rank = [0 for i in range(0, len(values1))]for p in range(0,len(values1)):S[p]=[]n[p]=0for 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]):if q not in S[p]:S[p].append(q)elif (values1[q] > values1[p] and values2[q] > values2[p]) or(values1[q] >= values1[p] and values2[q] > values2[p]) or(values1[q] > values1[p] and values2[q] >= values2[p]):n[p] = n[p] + 1if n[p]==0:rank[p] = 0if p not in front[0]:front[0].append(p)i = 0while(front[i] != []):Q=[]for p in front[i]:for q in S[p]:n[q] =n[q] - 1if( n[q]==0):rank[q]=i+1if q not in Q:Q.append(q)i = i+1front.append(Q)del front[len(front)-1]return front#Function to calculate crowding distance
def crowding_distance(values1, values2, front):distance = [0 for i in range(0,len(front))]sorted1 = sort_by_values(front, values1[:])sorted2 = sort_by_values(front, values2[:])distance[0] = 4444444444444444distance[len(front) - 1] = 4444444444444444for k in range(1,len(front)-1):distance[k] = distance[k]+ (values1[sorted1[k+1]] - values2[sorted1[k-1]])/(max(values1)-min(values1))for k in range(1,len(front)-1):distance[k] = distance[k]+ (values1[sorted2[k+1]] - values2[sorted2[k-1]])/(max(values2)-min(values2))return distance#Function to carry out the crossover
def crossover(a,b):r=random.random()if r>0.5:return mutation((a+b)/2)else:return mutation((a-b)/2)#Function to carry out the mutation operator
def mutation(solution):mutation_prob = random.random()if mutation_prob <1:solution = min_x+(max_x-min_x)*random.random()return solution#Main program starts here
pop_size = 20
max_gen = 921#Initialization
min_x=-55
max_x=55
# 随机生成初始种群
solution=[min_x+(max_x-min_x)*random.random() for i in range(0,pop_size)]
gen_no=0
while(gen_no<max_gen):# 自适应度计算function1_values = [function1(solution[i])for i in range(0,pop_size)]function2_values = [function2(solution[i])for i in range(0,pop_size)]# pareto等级non_dominated_sorted_solution = fast_non_dominated_sort(function1_values[:],function2_values[:])print("The best front for Generation number ",gen_no, " is")for valuez in non_dominated_sorted_solution[0]:print(round(solution[valuez],3),end=" ")print("
")# 拥挤度距离计算crowding_distance_values = []for i in range(0,len(non_dominated_sorted_solution)):crowding_distance_values.append(crowding_distance(function1_values[:],function2_values[:],non_dominated_sorted_solution[i][:]))solution2 = solution[:] # P+Q#Generating offspringswhile(len(solution2)!=2*pop_size):a1 = random.randint(0,pop_size-1)b1 = random.randint(0,pop_size-1)# 交叉变异solution2.append(crossover(solution[a1],solution[b1]))# 计算 P+Q种群的适应度function1_values2 = [function1(solution2[i])for i in range(0,2*pop_size)]function2_values2 = [function2(solution2[i])for i in range(0,2*pop_size)]# 非支配排序non_dominated_sorted_solution2 = fast_non_dominated_sort(function1_values2[:],function2_values2[:])# 拥挤度距离计算crowding_distance_values2=[]for i in range(0,len(non_dominated_sorted_solution2)):crowding_distance_values2.append(crowding_distance(function1_values2[:],function2_values2[:],non_dominated_sorted_solution2[i][:]))# 得到下一代种群P1new_solution = []   # indexfor i in range(0,len(non_dominated_sorted_solution2)):non_dominated_sorted_solution2_1 = [index_of(non_dominated_sorted_solution2[i][j],non_dominated_sorted_solution2[i]) for j in range(0,len(non_dominated_sorted_solution2[i]))]front22 = sort_by_values(non_dominated_sorted_solution2_1[:], crowding_distance_values2[i][:])front = [non_dominated_sorted_solution2[i][front22[j]] for j in range(0,len(non_dominated_sorted_solution2[i]))]front.reverse()for value in front:new_solution.append(value)if(len(new_solution)==pop_size):breakif (len(new_solution) == pop_size):breaksolution = [solution2[i] for i in new_solution]gen_no = gen_no + 1#Lets plot the final front now
function1 = [i * -1 for i in function1_values]
function2 = [j * -1 for j in function2_values]
plt.xlabel('Function 1', fontsize=15)
plt.ylabel('Function 2', fontsize=15)
plt.scatter(function1, function2)
plt.show()

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