请在以上代码中添加一个可视化模块

好的，我们可以使用matplotlib模块来添加可视化功能。具体地，我们可以在每一代结束后，绘制种群中个体的适应度分布图，以便更好地了解遗传算法的优化过程。

以下是修改后的代码：

import random
import matplotlib.pyplot as plt

# 定义图的邻接矩阵
graph = [
    [0, 1, 0, 1],
    [1, 0, 1, 1],
    [0, 1, 0, 1],
    [1, 1, 1, 0]
]

# 定义遗传算法参数
POPULATION_SIZE = 10  # 种群大小
GENERATIONS = 100  # 迭代次数
MUTATION_RATE = 0.1  # 变异概率


def calculate_fitness(individual):
    """
    计算个体的适应度
    """
    fitness = 0
    for i in range(len(graph)):
        for j in range(i+1, len(graph)):
            if graph[i][j] and individual[i] != individual[j]:
                fitness += 1
    return fitness


def create_individual():
    """
    生成一个随机的个体
    """
    return [random.choice([0, 1]) for _ in range(len(graph))]


def crossover(parent1, parent2):
    """
    交叉操作
    """
    crossover_point = random.randint(0, len(graph)-1)
    child1 = parent1[:crossover_point] + parent2[crossover_point:]
    child2 = parent2[:crossover_point] + parent1[crossover_point:]
    return child1, child2


def mutate(individual):
    """
    变异操作
    """
    for i in range(len(individual)):
        if random.random() < MUTATION_RATE:
            individual[i] = 1 - individual[i]
    return individual


def select_parents(population):
    """
    选择操作
    """
    fitnesses = [calculate_fitness(individual) for individual in population]
    total_fitness = sum(fitnesses)
    probabilities = [fitness/total_fitness for fitness in fitnesses]
    parent1 = random.choices(population, probabilities)[0]
    parent2 = random.choices(population, probabilities)[0]
    return parent1, parent2


# 初始化种群
population = [create_individual() for _ in range(POPULATION_SIZE)]

# 进化过程
fitness_history = []
for generation in range(GENERATIONS):
    # 计算适应度并统计历史
    fitnesses = [calculate_fitness(individual) for individual in population]
    fitness_history.append((max(fitnesses), sum(fitnesses)/len(fitnesses)))

    # 选择下一代
    new_population = []
    for _ in range(POPULATION_SIZE):
        parent1, parent2 = select_parents(population)
        child1, child2 = crossover(parent1, parent2)
        child1 = mutate(child1)
        child2 = mutate(child2)
        new_population.append(child1)
        new_population.append(child2)

    # 更新种群
    population = new_population

    # 输出最优解
    best_individual = max(population, key=calculate_fitness)
    print("Generation {}: Best Fitness = {}".format(generation+1, calculate_fitness(best_individual)))
    print("Solution: {}".format(best_individual))

# 绘制适应度分布图
max_fitnesses, avg_fitnesses = zip(*fitness_history)
plt.plot(max_fitnesses, label='Max Fitness')
plt.plot(avg_fitnesses, label='Avg Fitness')
plt.xlabel('Generation')
plt.ylabel('Fitness')
plt.legend()
plt.show()

在上述代码中，我们添加了一个fitness_history列表，用于记录每一代种群的最大适应度和平均适应度。在每一代结束时，我们计算适应度并将其添加到fitness_history中。

在主函数结束时，我们使用matplotlib模块绘制适应度分布图，以便更好地了解遗传算法的优化过程。绘制出的图形将最大适应度和平均适应度分别作为红色和蓝色曲线进行展示。

这样，我们就成功地在遗传算法中添加了可视化功能，以便更好地了解算法的优化过程。