用python写一个NSGA2的代码

以下一个简单的Python实现NSGA-II算法的代码，其中包含了一些基本的函数，例如计算适应度、交叉、变异和选择等。

import random

# 定义目标函数
def objective_function(x):
    return x[0]**2 + x[1]**2

# 定义种群数量
POPULATION_SIZE = 100

# 定义变量范围
LOWER_BOUND = [-5, -5]
UPPER_BOUND = [5, 5]

# 定义交叉概率
CROSSOVER_PROBABILITY = 0.9

# 定义变异概率
MUTATION_PROBABILITY = 0.1

# 定义最大迭代次数
MAX_GENERATIONS = 100

# 初始化种群
def initialize_population():
    population = []
    for i in range(POPULATION_SIZE):
        individual = []
        for j in range(len(LOWER_BOUND)):
            individual.append(random.uniform(LOWER_BOUND[j], UPPER_BOUND[j]))
        population.append(individual)
    return population

# 计算适应度
def calculate_fitness(population):
    fitness = []
    for individual in population:
        fitness.append(objective_function(individual))
    return fitness

# 选择操作
def select(population, fitness):
    # 非支配排序
    ranks = non_dominated_sort(population, fitness)
    # 计算拥挤度
    crowding_distances = crowding_distance(population, ranks)
    # 选择
    selected_population = []
    for i in range(POPULATION_SIZE):
        # 随机选择两个个体
        parent1 = random.choice(ranks)
        parent2 = random.choice(ranks)
        # 如果两个个体所在的等级相同，就比较它们的拥挤度
        if parent1 == parent2:
            if crowding_distances[parent1] > crowding_distances[parent2]:
                selected_population.append(population[parent1])
            else:
                selected_population.append(population[parent2])
        # 如果两个个体所在的等级不同，就选择等级较低的
        elif parent1 < parent2:
            selected_population.append(population[parent1])
        else:
            selected_population.append(population[parent2])
    return selected_population

# 非支配排序
def non_dominated_sort(population, fitness):
    # 初始化
    ranks = []
    S = {}
    n = {}
    # 初始化每个个体的支配集合和被支配数量
    for p in range(len(population)):
        S[p] = []
        n[p] = 0
        # 计算每个个体的支配关系
        for q in range(len(population)):
            if fitness[p] < fitness[q]:
                S[p].append(q)
            elif fitness[p] > fitness[q]:
                n[p] += 1
        # 如果p没有被任何个体支配，就是第一等级的个体
        if n[p] == 0:
            ranks.append(p)
    # 初始化等级
    i = 0
    # 进行非支配排序
    while ranks:
        i += 1
        Q = []
        for p in ranks:
            for q in S[p]:
                n[q] -= 1
                if n[q] == 0:
                    Q.append(q)
        ranks = Q
    return i-1

# 计算拥挤度
def crowding_distance(population, ranks):
    # 初始化拥挤度
    crowding_distances = {}
    # 每个等级的个体数
    num_ranks = len(set(ranks))
    # 计算每个等级的拥挤度
    for i in range(num_ranks):
        # 当前等级的个体
        rank_i = [j for j in range(len(population)) if ranks[j] == i]
        # 当前等级的个体数
        num_rank_i = len(rank_i)
        # 如果当前等级的个体数为0，就跳过
        if num_rank_i == 0:
            continue
        # 计算每个目标函数的最大值和最小值
        max_fitness = [max([population[j][k] for j in rank_i]) for k in range(len(population[0]))]
        min_fitness = [min([population[j][k] for j in rank_i]) for k in range(len(population[0]))]
        # 对每个个体按照每个目标函数进行排序
        sorted_rank_i = sorted(rank_i, key=lambda x: [population[x][k] for k in range(len(population[0]))])
        # 给第一个和最后一个个体的拥挤度赋值为无穷大
        crowding_distances[sorted_rank_i[0]] = float('inf')
        crowding_distances[sorted_rank_i[-1]] = float('inf')
        # 计算每个个体的拥挤度
        for j in range(1, num_rank_i-1):
            crowding_distances[sorted_rank_i[j]] = (population[sorted_rank_i[j+1]][i] - population[sorted_rank_i[j-1]][i]) / (max_fitness[i] - min_fitness[i])
    return crowding_distances

# 交叉操作
def crossover(parent1, parent2):
    # 随机选择交叉点
    crossover_point = random.randint(1, len(parent1)-1)
    # 交叉
    child1 = parent1[:crossover_point] + parent2[crossover_point:]
    child2 = parent2[:crossover_point] + parent1[crossover_point:]
    return child1, child2

# 变异操作
def mutation(individual):
    # 随机选择变异位置
    mutation_point = random.randint(0, len(individual)-1)
    # 变异
    individual[mutation_point] = random.uniform(LOWER_BOUND[mutation_point], UPPER_BOUND[mutation_point])
    return individual

# 主函数
def main():
    # 初始化种群
    population = initialize_population()
    # 进行迭代
    for generation in range(MAX_GENERATIONS):
        print('Generation:', generation+1)
        # 计算适应度
        fitness = calculate_fitness(population)
        # 选择操作
        selected_population = select(population, fitness)
        # 交叉操作
        offspring_population = []
        for i in range(0, POPULATION_SIZE-1, 2):
            parent1 = selected_population[i]
            parent2 = selected_population[i+1]
            if random.random() < CROSSOVER_PROBABILITY:
                child1, child2 = crossover(parent1, parent2)
            else:
                child1, child2 = parent1, parent2
            # 变异操作
            if random.random() < MUTATION_PROBABILITY:
                child1 = mutation(child1)
            if random.random() < MUTATION_PROBABILITY:
                child2 = mutation(child2)
            offspring_population.append(child1)
            offspring_population.append(child2)
        # 更新种群
        population = offspring_population

if __name__ == '__main__':
    main()

请注意，这只是一个简单的实现，可能不够高效或准确。如果您想要更好的NSGA-II实现，建议使用现有的Python库，例如DEAP或PyGMO。