python实现NSGAIII算法

NSGA-III是一种多目标优化算法，它是NSGA-II的改进版，主要用于解决多目标优化问题。下面是Python实现NSGA-III算法的步骤：

1. 安装必要的Python库，如numpy、matplotlib、pandas等。

2. 定义问题的目标函数和约束条件。

3. 初始化种群，可以使用随机数生成初始种群。

4. 计算每个个体的适应度值。

5. 根据适应度值对种群进行排序。

6. 选择优秀的个体进行交叉和变异操作，生成新的个体。

7. 计算新个体的适应度值。

8. 将新个体加入种群中。

9. 根据适应度值对种群进行排序。

10. 选择最优的个体作为解决方案。

下面是Python实现NSGA-III算法的示例代码：

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# 定义目标函数和约束条件
def obj_func(x):
    f1 = x[0]**2 + x[1]**2
    f2 = (x[0]-1)**2 + x[1]**2
    return [f1, f2]

def constraint(x):
    if x[0] + x[1] - 1.5 > 0:
        return False
    else:
        return True

# 初始化种群
def init_population(pop_size, num_var):
    population = np.random.rand(pop_size, num_var)
    return population

# 计算适应度值
def fitness(population):
    fitness_values = []
    for i in range(len(population)):
        if constraint(population[i]):
            fitness_values.append(obj_func(population[i]))
        else:
            fitness_values.append([float('inf'), float('inf')])
    return np.array(fitness_values)

# 快速非支配排序
def fast_non_dominated_sort(fitness_values):
    S = [[] for i in range(len(fitness_values))]
    front = [[]]
    n = [0 for i in range(len(fitness_values))]
    rank = [0 for i in range(len(fitness_values))]
    for p in range(len(fitness_values)):
        for q in range(len(fitness_values)):
            if (fitness_values[p][0] < fitness_values[q][0] and fitness_values[p][1] < fitness_values[q][1]):
                if q not in S[p]:
                    S[p].append(q)
            elif (fitness_values[q][0] < fitness_values[p][0] and fitness_values[q][1] < fitness_values[p][1]):
                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] -= 1
                if (n[q] == 0):
                    rank[q] = i + 1
                    if q not in Q:
                        Q.append(q)
        i += 1
        front.append(Q)
    del front[len(front)-1]
    return front

# 计算拥挤度
def crowding_distance(fitness_values, front):
    distance = [0 for i in range(len(fitness_values))]
    for f in front:
        f_fitness = fitness_values[f]
        sorted_f = [x for _,x in sorted(zip(f_fitness, f))]
        distance[sorted_f[0]] = float('inf')
        distance[sorted_f[-1]] = float('inf')
        for i in range(1, len(sorted_f)-1):
            distance[sorted_f[i]] += (sorted_f[i+1][0] - sorted_f[i-1][0])/(max(fitness_values[:,0])-min(fitness_values[:,0]))
    return distance

# 选择操作
def selection(population, fitness_values, num_parents):
    parents = np.empty((num_parents, population.shape[1]))
    for i in range(num_parents):
        front = fast_non_dominated_sort(fitness_values)[0]
        crowding_dist = crowding_distance(fitness_values, front)
        index = np.argmax(crowding_dist)
        parents[i,:] = population[front[index]]
        fitness_values[front[index]] = [-1,-1]
    return parents

# 交叉操作
def crossover(parents, offspring_size):
    offspring = np.empty(offspring_size)
    for i in range(offspring_size[0]):
        parent1_idx = i % parents.shape[0]
        parent2_idx = (i+1) % parents.shape[0]
        crossover_point = np.random.randint(1, offspring_size[1]-1)
        offspring[i, 0:crossover_point] = parents[parent1_idx, 0:crossover_point]
        offspring[i, crossover_point:] = parents[parent2_idx, crossover_point:]
    return offspring

# 变异操作
def mutation(offspring_crossover):
    for i in range(offspring_crossover.shape[0]):
        mutation_point = np.random.randint(0, offspring_crossover.shape[1]-1)
        offspring_crossover[i, mutation_point] = np.random.rand()
    return offspring_crossover

# NSGA-III算法
def nsga3(pop_size, num_var, num_obj, num_gen):
    population = init_population(pop_size, num_var)
    for i in range(num_gen):
        fitness_values = fitness(population)
        parents = selection(population, fitness_values, pop_size//2)
        offspring_crossover = crossover(parents, offspring_size=(pop_size-parents.shape[0], num_var))
        offspring_mutation = mutation(offspring_crossover)
        population = np.vstack((parents, offspring_mutation))
    fitness_values = fitness(population)
    front = fast_non_dominated_sort(fitness_values)[0]
    crowding_dist = crowding_distance(fitness_values, front)
    index = np.argsort(-crowding_dist)
    selected = index[:pop_size]
    return population[selected]

# 示例
pop_size = 100
num_var = 2
num_obj = 2
num_gen = 100
result = nsga3(pop_size, num_var, num_obj, num_gen)
print(result)

# 相关问题：
--相关问题--: