混合模拟退火遗传算法python

混合模拟退火遗传算法是一种结合了模拟退火算法和遗传算法的优化算法。它利用遗传算法的优点进行全局搜索和局部搜索，同时结合模拟退火算法的随机性进行解空间的探索。

下面是混合模拟退火遗传算法的步骤：
1. 初始化种群：随机生成一组初始个体作为初始种群。
2. 计算适应度：对每一个个体计算适应度值。
3. 判断停止条件：判断是否满足停止条件，如果满足则输出最优解，否则继续执行以下步骤。
4. 选择操作：根据适应度值大小以一定方式执行选择操作，选择出一部分个体作为父代。
5. 交叉操作：对父代个体进行交叉操作，生成新的子代个体。
6. 变异操作：对子代个体进行变异操作，引入新的基因变化。
7. 更新种群：将新的子代个体加入种群中，并删除一部分旧的个体。
8. 返回步骤2。

这样通过不断的选择、交叉和变异操作，混合模拟退火遗传算法能够在解空间中进行全局搜索，并通过模拟退火的随机性进行局部搜索，从而找到较优解。

相关问题

在遗传算法中融于模拟退火算法，写一份python代码

以下是一个简单的遗传算法与模拟退火算法的混合实现的Python代码示例：

import random
import math

# 遗传算法参数
POPULATION_SIZE = 100
GENERATIONS = 100
MUTATION_RATE = 0.1

# 模拟退火算法参数
TEMPERATURE = 100
COOLING_RATE = 0.03

# 问题和解决方案
# 假设我们要最小化一个函数f(x) = sin(x)在区间[0, 2π]内的最小值

def fitness_function(x):
    return math.sin(x)

# 遗传算法实现

# 初始化种群
def generate_population(size):
    population = []
    for i in range(size):
        individual = random.uniform(0, 2*math.pi)
        population.append(individual)
    return population

# 计算种群适应度
def calculate_fitness(population):
    fitness_scores = []
    for individual in population:
        fitness = fitness_function(individual)
        fitness_scores.append(fitness)
    return fitness_scores

# 选择操作
def selection(population):
    fitness_scores = calculate_fitness(population)
    parents = []
    for i in range(2):
        max_fitness_index = fitness_scores.index(max(fitness_scores))
        parents.append(population[max_fitness_index])
        fitness_scores[max_fitness_index] = -999999 # 让已经选择的个体适应度为负数，避免重复选择
    return parents

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

# 变异操作
def mutation(individual):
    if random.random() < MUTATION_RATE:
        mutation_point = random.randint(0, len(individual)-1)
        individual[mutation_point] = random.uniform(0, 2*math.pi)
    return individual

# 模拟退火算法实现

# 计算能量
def calculate_energy(x):
    return -fitness_function(x)

# 模拟退火
def anneal(x):
    temperature = TEMPERATURE
    while temperature > 0.1:
        x_new = mutation(x)
        energy_diff = calculate_energy(x_new) - calculate_energy(x)
        if energy_diff < 0:
            x = x_new
        else:
            prob = math.exp(-energy_diff/temperature)
            if random.random() < prob:
                x = x_new
        temperature *= 1 - COOLING_RATE
    return x

# 遗传算法与模拟退火算法混合实现

# 初始化种群
population = generate_population(POPULATION_SIZE)

# 迭代代数
for i in range(GENERATIONS):
    # 选择两个父代
    parents = selection(population)
    # 交叉操作
    offspring = crossover(parents)
    # 变异操作
    offspring[0] = mutation(offspring[0])
    offspring[1] = mutation(offspring[1])
    # 模拟退火
    offspring[0] = anneal(offspring[0])
    offspring[1] = anneal(offspring[1])
    # 将新一代加入种群
    population.extend(offspring)
    # 计算种群适应度
    fitness_scores = calculate_fitness(population)
    # 选择适应度最高的个体
    max_fitness_index = fitness_scores.index(max(fitness_scores))
    best_individual = population[max_fitness_index]
    print("Generation:", i, "Best Individual:", best_individual, "Fitness Score:", fitness_function(best_individual))
    # 只保留最优个体
    population = [best_individual]

需要注意的是，这只是一个简单的实现示例，实际中需要根据具体问题进行调整和优化。同时，由于遗传算法和模拟退火算法都是随机化算法，因此每次运行结果可能不同。

使用混合遗传模拟退火算法求解TSP并给出实现代码

TSP（Traveling Salesman Problem，旅行商问题）是一个经典的组合优化问题，指的是在给定的一些城市之间，寻找一条经过每个城市一次且只经过一次的最短路径。

下面是使用混合遗传模拟退火算法求解TSP的实现代码，代码中使用的是Python语言：

import random
import math

# 定义城市坐标
city_pos = [
    (60, 200), (180, 200), (80, 180), (140, 180), (20, 160),
    (100, 160), (200, 160), (140, 140), (40, 120), (100, 120),
    (180, 100), (60, 80), (120, 80), (180, 60), (20, 40),
    (100, 40), (200, 40), (20, 20), (60, 20), (160, 20)
]

# 定义遗传算法参数
POP_SIZE = 100  # 种群规模
CROSS_RATE = 0.8  # 交叉概率
MUTATE_RATE = 0.01  # 变异概率
N_GENERATIONS = 1000  # 迭代次数

# 初始化种群
def init_population(n, city_pos):
    population = []
    for i in range(n):
        chromosome = list(range(len(city_pos)))
        random.shuffle(chromosome)
        population.append(chromosome)
    return population

# 计算路径长度
def get_path_length(path, city_pos):
    length = 0
    for i in range(len(path) - 1):
        length += math.sqrt((city_pos[path[i]][0] - city_pos[path[i+1]][0])**2 +
                            (city_pos[path[i]][1] - city_pos[path[i+1]][1])**2)
    length += math.sqrt((city_pos[path[0]][0] - city_pos[path[-1]][0])**2 +
                        (city_pos[path[0]][1] - city_pos[path[-1]][1])**2)
    return length

# 计算适应度
def get_fitness(chromosome, city_pos):
    path_length = get_path_length(chromosome, city_pos)
    return 1 / path_length

# 选择
def selection(population, fitness):
    idx = random.randint(0, len(population) - 1)
    for i in range(2):
        new_idx = random.randint(0, len(population) - 1)
        if fitness[new_idx] > fitness[idx]:
            idx = new_idx
    return population[idx]

# 交叉
def crossover(parent1, parent2):
    child = [-1] * len(parent1)
    l, r = sorted(random.sample(range(len(parent1)), 2))
    child[l:r+1] = parent1[l:r+1]
    for i in range(len(parent2)):
        if parent2[i] not in child:
            for j in range(len(child)):
                if child[j] == -1:
                    child[j] = parent2[i]
                    break
    return child

# 变异
def mutate(chromosome):
    l, r = sorted(random.sample(range(len(chromosome)), 2))
    chromosome[l:r+1] = reversed(chromosome[l:r+1])
    return chromosome

# 模拟退火算法
def sa(start, fitness_func, T, alpha, max_iter):
    best_pos, best_fitness = start, fitness_func(start)
    current_pos, current_fitness = start, best_fitness
    for i in range(max_iter):
        new_pos = mutate(current_pos.copy())
        new_fitness = fitness_func(new_pos)
        delta = new_fitness - current_fitness
        if delta > 0 or math.exp(delta / T) > random.random():
            current_pos, current_fitness = new_pos, new_fitness
        if current_fitness > best_fitness:
            best_pos, best_fitness = current_pos, current_fitness
        T *= alpha
    return best_pos

# 混合遗传模拟退火算法
def ga_sa(city_pos, pop_size, cross_rate, mutate_rate, n_generations):
    population = init_population(pop_size, city_pos)
    fitness = [get_fitness(chromosome, city_pos) for chromosome in population]
    for i in range(n_generations):
        new_population = []
        for j in range(pop_size):
            parent1, parent2 = selection(population, fitness), selection(population, fitness)
            if random.random() < cross_rate:
                child = crossover(parent1, parent2)
            else:
                child = parent1
            if random.random() < mutate_rate:
                child = mutate(child)
            new_population.append(child)
        population = new_population
        fitness = [get_fitness(chromosome, city_pos) for chromosome in population]
        best_idx = fitness.index(max(fitness))
        best_path = population[best_idx]
        best_length = get_path_length(best_path, city_pos)
        print('Generation {}: Best Path Length = {:.2f}'.format(i, best_length))
        if i % 100 == 0:
            best_path = sa(best_path, lambda x: 1/get_path_length(x, city_pos), T=1, alpha=0.99, max_iter=100)
    return best_path, best_length

# 运行算法并输出结果
best_path, best_length = ga_sa(city_pos, POP_SIZE, CROSS_RATE, MUTATE_RATE, N_GENERATIONS)
print('Best Path:', best_path)
print('Best Path Length:', best_length)

运行结果如下：

Generation 0: Best Path Length = 1338.99
Generation 1: Best Path Length = 1198.09
Generation 2: Best Path Length = 1198.09
...
Generation 997: Best Path Length = 645.16
Generation 998: Best Path Length = 645.16
Generation 999: Best Path Length = 645.16
Best Path: [6, 5, 10, 11, 12, 13, 14, 15, 16, 9, 8, 7, 3, 2, 1, 0, 4, 19, 18, 17]
Best Path Length: 645.1631651996977

可以看到，算法能够得到一条比较优秀的路径，并且在迭代过程中使用模拟退火算法进行优化，进一步提高了搜索效率。