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^2
        f2(X) = -(x-2)^2
    s.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**2
    return value

#Second function to optimize
def function2(x):
    value = -(x-2)**2
    return value

#Function to find index of list
def index_of(a,list):
    for i in range(0,len(list)):
        if list[i] == a:
            return i
    return -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.inf
    return 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]=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]):
                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] + 1
        if n[p]==0:
            rank[p] = 0
            if p not in front[0]:
                front[0].append(p)

    i = 0
    while(front[i] != []):
        Q=[]
        for p in front[i]:
            for q in S[p]:
                n[q] =n[q] - 1
                if( n[q]==0):
                    rank[q]=i+1
                    if q not in Q:
                        Q.append(q)
        i = i+1
        front.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] = 4444444444444444
    distance[len(front) - 1] = 4444444444444444
    for 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