用A*算法、爬山法、遗传算法解决旅行商问题
编写TSP（旅行商问题）的实例生成器，城市的位置用在单位正方形内的随机点表示。并分别用A*算法与爬山法、遗传算法来求解TSP问题实例。
以下是具体题目要求，用c++、python、java都可以！要标明并附上代码！
TechWhizKid参考GPT回答：
以下是使用A*算法、爬山法和遗传算法解决旅行商问题的示例代码：
A*算法：
import heapq
# 定义城市类
class City:
def __init__(self, name, x, y):
self.name = name
self.x = x
self.y = y
def __str__(self):
return self.name
# 计算两个城市之间的距离
def calculate_distance(city1, city2):
return ((city2.x - city1.x) ** 2 + (city2.y - city1.y) ** 2) ** 0.5
# A*算法求解TSP问题
def solve_tsp_A_star(cities, start_city):
# 定义优先队列
pq = []
heapq.heappush(pq, (0, [start_city], set()))
while pq:
cost, path, visited = heapq.heappop(pq)
current_city = path[-1]
# 判断是否已经访问过所有城市
if len(path) == len(cities):
return path, cost
for city in cities:
if city != current_city and city not in visited:
new_cost = cost + calculate_distance(current_city, city)
heuristic = calculate_distance(city, start_city)
heapq.heappush(pq, (new_cost + heuristic, path + [city], visited | {city}))
return None
# 示例生成器：生成随机城市列表
def generate_cities(num_cities):
import random
cities = []
for i in range(num_cities):
name = chr(ord('A') + i)
x = random.random()
y = random.random()
cities.append(City(name, x, y))
return cities
# 测试示例
cities = generate_cities(5)
start_city = cities[0]
path, cost = solve_tsp_A_star(cities, start_city)
print("Path:", ' -> '.join(str(city) for city in path))
print("Total Cost:", cost)
爬山法：
import random
# 评估路径的总距离
def evaluate_path(cities, path):
total_distance = 0
for i in range(len(path)):
city1 = path[i]
city2 = path[(i + 1) % len(path)]
total_distance += calculate_distance(cities[city1], cities[city2])
return total_distance
# 随机生成初始路径
def generate_initial_path(num_cities):
path = list(range(num_cities))
random.shuffle(path)
return path
# 爬山法求解TSP问题
def solve_tsp_hill_climbing(cities):
num_cities = len(cities)
current_path = generate_initial_path(num_cities)
current_cost = evaluate_path(cities, current_path)
while True:
neighbors = []
for i in range(num_cities):
for j in range(i + 1, num_cities):
neighbor = current_path.copy()
neighbor[i], neighbor[j] = neighbor[j], neighbor[i]
neighbors.append(neighbor)
best_neighbor = None
best_neighbor_cost = float('inf')
for neighbor in neighbors:
neighbor_cost = evaluate_path(cities, neighbor)
if neighbor_cost < best_neighbor_cost:
best_neighbor = neighbor
best_neighbor_cost = neighbor_cost
if best_neighbor_cost < current_cost:
current_path = best_neighbor
current_cost = best_neighbor_cost
else:
break
return current_path, current_cost
# 测试示例
cities = generate_cities(5)
path, cost = solve_tsp_hill_climbing(cities)
print("Path:", ' -> '.join(cities[i].name for i in path))
print("Total Cost:", cost)
遗传算法：
import random
# 生成初始种群
def generate_initial_population(num_cities, population_size):
population = []
for _ in range(population_size):
path = list(range(num_cities))
random.shuffle(path)
population.append(path)
return population
# 评估个体路径的适应度（倒数距离）
def evaluate_fitness(cities, path):
distance = evaluate_path(cities, path)
return 1 / distance
# 选择父代个体
def selection(population, fitness):
# 使用轮盘赌选择方法
total_fitness = sum(fitness)
probabilities = [fit / total_fitness for fit in fitness]
selected_indices = random.choices(range(len(population)), probabilities, k=2)
return [population[idx] for idx in selected_indices]
# 交叉生成子代个体
def crossover(parent1, parent2):
# 使用顺序交叉算子
num_cities = len(parent1)
start = random.randint(0, num_cities - 2)
end = random.randint(start + 1, num_cities - 1)
child = [-1] * num_cities
# 保留父代1的部分路径
for i in range(start, end + 1):
child[i] = parent1[i]
# 填充子代剩余部分
index = 0
for i in range(num_cities):
if child[index] == -1:
while parent2[index] in child:
index = (index + 1) % num_cities
child[index] = parent2[index]
index = (index + 1) % num_cities
return child
# 变异个体
def mutate(individual):
# 使用交换变异算子
index1 = random.randint(0, len(individual) - 1)
index2 = random.randint(0, len(individual) - 1)
individual[index1], individual[index2] = individual[index2], individual[index1]
return individual
# 遗传算法求解TSP问题
def solve_tsp_genetic(cities, population_size, num_generations):
num_cities = len(cities)
population = generate_initial_population(num_cities, population_size)
best_path = None
best_cost = float('inf')
for _ in range(num_generations):
fitness = [evaluate_fitness(cities, path) for path in population]
for i in range(population_size):
if fitness[i] > best_cost:
best_path = population[i]
best_cost = fitness[i]
new_population = [best_path]
while len(new_population) < population_size:
parent1, parent2 = selection(population, fitness)
child = crossover(parent1, parent2)
child = mutate(child)
new_population.append(child)
population = new_population
return best_path, 1 / best_cost
# 测试
示例
cities = generate_cities(5)
path, cost = solve_tsp_genetic(cities, population_size=10, num_generations=100)
print("Path:", ' -> '.join(cities[i].name for i in path))
print("Total Cost:", cost)
4.3
import random
# 评估路径的总距离
def evaluate_path(cities, path):
total_distance = 0
for i in range(len(path)):
city1 = path[i]
city2 = path[(i + 1) % len(path)]
total_distance += calculate_distance(cities[city1], cities[city2])
return total_distance
# 随机生成初始路径
def generate_initial_path(num_cities):
path = list(range(num_cities))
random.shuffle(path)
return path
# 爬山法求解TSP问题
def solve_tsp_hill_climbing(cities):
num_cities = len(cities)
current_path = generate_initial_path(num_cities)
current_cost = evaluate_path(cities, current_path)
while True:
neighbors = []
for i in range(num_cities):
for j in range(i + 1, num_cities):
neighbor = current_path.copy()
neighbor[i], neighbor[j] = neighbor[j], neighbor[i]
neighbors.append(neighbor)
best_neighbor = None
best_neighbor_cost = float('inf')
for neighbor in neighbors:
neighbor_cost = evaluate_path(cities, neighbor)
if neighbor_cost < best_neighbor_cost:
best_neighbor = neighbor
best_neighbor_cost = neighbor_cost
if best_neighbor_cost < current_cost:
current_path = best_neighbor
current_cost = best_neighbor_cost
else:
break
return current_path, current_cost
# 使用MST启发式的A*算法求解TSP问题
def solve_tsp_A_star_MST(cities, start_city):
# 构建MST
def build_MST(cities):
visited = set()
mst = []
current_city = start_city
visited.add(current_city)
while len(visited) < len(cities):
min_distance = float('inf')
nearest_city = None
for city in cities:
if city != current_city and city not in visited:
distance = calculate_distance(current_city, city)
if distance < min_distance:
min_distance = distance
nearest_city = city
mst.append((current_city, nearest_city))
visited.add(nearest_city)
current_city = nearest_city
return mst
# 计算MST的总代价
def calculate_MST_cost(mst):
total_cost = 0
for edge in mst:
total_cost += calculate_distance(edge[0], edge[1])
return total_cost
# 启发式函数：剩余路径的最小生成树代价
def heuristic(city, visited):
remaining_cities = set(cities) - visited
remaining_mst = build_MST(remaining_cities)
remaining_cost = calculate_MST_cost(remaining_mst)
return remaining_cost
# A*算法求解TSP问题
def solve_tsp_A_star(cities, start_city):
pq = []
heapq.heappush(pq, (0, [start_city], set()))
while pq:
cost, path, visited = heapq.heappop(pq)
current_city = path[-1]
if len(path) == len(cities):
return path, cost
for city in cities:
if city != current_city and city not in visited:
new_cost = cost + calculate_distance(current_city, city)
h = heuristic(city, visited)
heapq.heappush(pq, (new_cost + h, path + [city], visited | {city}))
return None
mst = build_MST(cities)
mst_cost = calculate_MST_cost(mst)
path, cost = solve_tsp_A_star(cities, start_city)
return path, cost, mst_cost
# 测试示例
cities = generate_cities(5)
start_city = cities[0]
# 使用爬山法求解TSP问题
hill_climbing_path, hill_climbing_cost = solve_tsp_hill_climbing(cities)
# 使用MST启发式的A*算法求解TSP问题
a_star_path, a_star_cost, mst_cost = solve_tsp_A_star_MST(cities, start_city)
print("Hill Climbing Path:", ' -> '.join(cities[i].name for i in hill_climbing_path))
print("Hill Climbing Cost:", hill_climbing_cost)
print()
print("A* with MST Heuristic Path:", ' -> '.join(cities[i].name for i in a_star_path))
print("A* with MST Heuristic Cost:", a_star_cost)
print("Minimum Spanning Tree (MST) Cost:", mst_cost)
- 给你找了一篇非常好的博客，你可以看看是否有帮助，链接：TSP路径规划总结（常用解决方案 A*算法，蜂群算法，遗传算法，蚁群及其优化等）
- 除此之外, 这篇博客: 遗传算法对比模拟退火算法求解TSP问题（C++实现）中的 a.算法的结果 部分也许能够解决你的问题, 你可以仔细阅读以下内容或跳转源博客中阅读:
结果图表展示：
次数 最优解 误差 运行时间 1 584.16 3.57% 334.53s 2 590.01 4.60% 332.12s 3 580.63 2.95% 345.20s 4 589.41 4.50% 315.22s 5 589.82 4.58% 350.31s 6 582.49 3.28% 335.41s 7 584.25 3.54% 337.23s 8 582.97 3.36% 340.33s 9 585.35 3.78% 332.96s 10 585.20 3.75% 338.97s 根据上述十次测试结果可以得出
最好解：
路径长度为580.63，参考最优解为564，误差为2.95%。
最差解：
路径长度为590.01，参考最优解为564，误差为4.60%。
平均值：
路径长度为585.43，参考最优解为564，误差为3.79%
标准差：
3.28107
方差：
10.76541
算法的平均速度：
运行时间为335.8s
其中一次运行结果的解下降情况，横坐标是繁殖的代数，纵坐标为该代种群中的最优解
显示TSP路径的收敛情况
第一代：
最后一代：
有用麻烦点个采纳哦
这个博客给了源码，可以参考一下，
https://blog.csdn.net/qq_33950926/article/details/130046741
这是一项比较大的任务，我会给出一些代码示例，但是这个问题可能需要你自己做一些额外的工作和研究。以下是一个简单的Python示例，它生成了TSP问题的实例，并使用遗传算法来求解。这个示例使用了deap库来实现遗传算法。
首先，我们安装需要使用的库：
pip install deap numpy matplotlib
然后，编写TSP问题的实例生成器和遗传算法求解器：
import random
import numpy as np
import matplotlib.pyplot as plt
from deap import algorithms, base, creator, tools
# 创建城市位置
num_cities = 20
cities = [random.sample(range(100), 2) for _ in range(num_cities)]
distances = np.empty((num_cities, num_cities))
for i in range(num_cities):
for j in range(num_cities):
# 计算城市间的欧氏距离
distances[i, j] = np.sqrt((cities[i][0] - cities[j][0]) ** 2 + (cities[i][1] - cities[j][1]) ** 2)
# 创建问题类型
creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)
toolbox = base.Toolbox()
toolbox.register("indices", random.sample, range(num_cities), num_cities)
toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.indices)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
def evalTSP(individual):
# 计算旅行路径的总距离
return sum(distances[individual[i - 1], individual[i]] for i in range(num_cities)),
toolbox.register("mate", tools.cxPartialyMatched)
toolbox.register("mutate", tools.mutShuffleIndexes, indpb=0.05)
toolbox.register("select", tools.selTournament, tournsize=3)
toolbox.register("evaluate", evalTSP)
def main():
pop = toolbox.population(n=100)
hof = tools.HallOfFame(1)
stats = tools.Statistics(lambda ind: ind.fitness.values)
stats.register("avg", np.mean)
stats.register("std", np.std)
stats.register("min", np.min)
stats.register("max", np.max)
pop, logbook = algorithms.eaSimple(pop, toolbox, cxpb=0.7, mutpb=0.2, ngen=100,
stats=stats, halloffame=hof, verbose=True)
return pop, logbook, hof
if __name__ == "__main__":
pop, log, hof = main()
print("Best individual is: %s\nwith fitness: %s" % (hof[0], hof[0].fitness))
gen, avg, min_, max_ = log.select("gen", "avg", "min", "max")
plt.plot(gen, avg, label="average")
plt.plot(gen, min_, label="minimum")
plt.plot(gen, max_, label="maximum")
plt.xlabel("Generation")
plt.ylabel("Fitness")
plt.legend(loc="lower right")
plt.show()
这个示例生成了20个城市的位置，然后使用遗传算法来寻找最短的旅行路径。遗传算法的参数可能需要根据问题的具体情况进行调整。
至于A*算法和爬山法，你可能需要自己编写或者寻找现有的实现。这两种算法的实现通常比较复杂，需要理解算法的工作原理，并能够将这些原理转化为有效的代码。我建议你查阅相关的教科书或者在线教程，了解这些算法的工作原理和实现方法。