粒子群算法实现旅行商问题
粒子群算法（Particle Swarm Optimization, PSO）是一种基于群体智能的优化算法，它模拟了鸟群狩猎和食物捕捉的行为，通过不断迭代来寻找最优解
以下是使用Python实现的粒子群算法解决旅行商问题的示例代码：
```python
import numpy as np
import random
计算总距离
def calculate_total_distance(route, distance_matrix):
total_distance = 0
for i in range(len(route) - 1):
total_distance += distance_matrix[route[i]][route[i + 1]]
total_distance += distance_matrix[route[-1]][route[0]]
return total_distance
粒子群算法解决旅行商问题
def pso_tsp(distance_matrix, n_particles=20, n_iterations=100, w=0.9, c1=0.1, c2=0.1):
n_cities = len(distance_matrix)
particles = []
best_particles = []
global_best = None
初始化粒子
for _ in range(n_particles):
route = list(range(n_cities))
random.shuffle(route)
particles.append(route)
total_distance = calculate_total_distance(route, distance_matrix)
best_particles.append(route)
if global_best is None or total_distance < global_best[1]:
global_best = (route, total_distance)
迭代优化
for _ in range(n_iterations):
for i in range(n_particles):
更新粒子位置
particle = particles[i]
best_particle = best_particles[i]
for j in range(n_cities):
r1 = random.random()
r2 = random.random()
cognitive = c1 * r1 * (best_particle[j] - particle[j])
social = c2 * r2 * (global_best[0][j] - particle[j])
particle[j] += cognitive + social
修正粒子位置
for j in range(n_cities):
if particle[j] < 0:
particle[j] = -particle[j]
elif particle[j] >= n_cities:
particle[j] = n_cities - 1
计算当前粒子的总距离
total_distance = calculate_total_distance(particle, distance_matrix)
更新最佳粒子位置
if total_distance < calculate_total_distance(best_particles[i], distance_matrix):
best_particles[i] = particle.copy()
更新全局最佳位置
if total_distance < global_best[1]:
global_best = (particle.copy(), total_distance)
return global_best
示例距离矩阵
distance_matrix = [
[0, 10, 15, 20],
[10, 0, 35, 25],
[15, 35, 0, 30],
[20, 25, 30, 0]
]
运行粒子群算法
best_route, best_distance = pso_tsp(distance_matrix)
print("Best route:", best_route)
print("Best distance:", best_distance)
```
在这个示例中，我们定义了一个`calculate_total_distance`函数来计算给定路线的总距离。然后，我们实现了`pso_tsp`函数，该函数使用粒子群算法来寻找最短路径。我们提供了一个示例距离矩阵，并运行了粒子群算法来找到最佳路线。
粒子群算法解决路径问题编程
粒子群算法（Particle Swarm Optimization, PSO）是一种基于群体智能的优化算法，用于求解最优化问题
以下是一个使用Python实现的简单粒子群算法来解决旅行商问题（TSP）的示例：
```python
import numpy as np
import random
def tsp_distance(city1, city2):
return np.sqrt((city1[0] - city2[0]) 2 + (city1[1] - city2[1]) 2)
def total_distance(path, cities):
return sum(tsp_distance(cities[path[i]], cities[path[i - 1]]) for i in range(len(path)))
def pso_tsp(cities, num_particles=20, num_iterations=100, w=0.9, c1=0.1, c2=0.1):
num_cities = len(cities)
particles = [np.random.permutation(num_cities) for _ in range(num_particles)]
best_paths = [None] * num_particles
best_distances = [float("inf")] * num_particles
for i, particle in enumerate(particles):
distance = total_distance(particle, cities)
if distance < best_distances[i]:
best_paths[i] = particle.copy()
best_distances[i] = distance
global_best_path = best_paths[np.argmin(best_distances)]
global_best_distance = min(best_distances)
for _ in range(num_iterations):
for i, particle in enumerate(particles):
r1, r2 = random.random(), random.random()
velocity = w * particle + c1 * r1 * (best_paths[i] - particle) + c2 * r2 * (global_best_path - particle)
particle += velocity
确保粒子不会出现在城市之外
particle = np.clip(particle, 0, num_cities - 1)
distance = total_distance(particle, cities)
if distance < best_distances[i]:
best_paths[i] = particle.copy()
best_distances[i] = distance
if distance < global_best_distance:
global_best_path = particle.copy()
global_best_distance = distance
return global_best_path, global_best_distance
if __name__ == "__main__":
cities = np.array([[1, 1], [5, 1], [7, 5], [4, 6], [2, 4]])
path, distance = pso_tsp(cities)
print("Best path:", path)
print("Best distance:", distance)
```
这个示例中，我们定义了`tsp_distance`函数来计算两个城市之间的距离，`total_distance`函数来计算给定路径的总距离。`pso_tsp`函数实现了粒子群算法，参数包括城市列表、粒子数量、迭代次数以及粒子群算法的三个参数w、c1和c2。
在主程序中，我们定义了一个城市列表，然后调用`pso_tsp`函数来求解TSP问题。我们输出找到的最佳路径和对应的距离。
粒子群算法实现旅行商问题（粒子群算法解决路径问题编程）此文由小邹编辑，于2025-08-06 01:10:17发布在知识大全栏目，本文地址：粒子群算法实现旅行商问题（粒子群算法解决路径问题编程）http://www.qquuu.com/detail/show-23-79066.html