tsp旅行商模拟退火算法python路径画图

TSP问题是指在给定的一些城市之间，求解访问每个城市一次并回到起始城市的最短路径。模拟退火算法是一种全局优化算法，可以用于求解TSP问题。下面是使用Python实现TSP问题模拟退火算法并画出路径图的步骤：

1. 安装必要的库：numpy、matplotlib和tqdm。

2. 定义TSP问题的距离矩阵，例如：

   import numpy as np
   
   # 城市坐标
   cities = np.array([[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], [60, 20], [120, 20], [160, 20]])
   
   # 计算距离矩阵
   n_cities = len(cities)
   dist_mat = np.zeros((n_cities, n_cities))
   for i in range(n_cities):
       for j in range(i+1, n_cities):
           dist_mat[i][j] = dist_mat[j][i] = np.linalg.norm(cities[i]-cities[j])

3. 定义模拟退火算法的参数，例如：

   # 初始温度
   t = 1000
   # 终止温度
   t_min = 1e-8
   # 降温速率
   alpha = 0.999
   # 迭代次数
   n_iter = 10000

4. 定义模拟退火算法的主函数，例如：

   def tsp_sa(dist_mat, t, t_min, alpha, n_iter):
       # 随机生成初始解
       cur_solution = np.random.permutation(len(dist_mat))
       cur_cost = get_cost(cur_solution, dist_mat)
       best_solution = cur_solution.copy()
       best_cost = cur_cost
       # 迭代
       for i in tqdm(range(n_iter)):
           # 生成新解
           new_solution = get_neighbor(cur_solution)
           new_cost = get_cost(new_solution, dist_mat)
           # 判断是否接受新解
           delta_cost = new_cost - cur_cost
           if delta_cost < 0 or np.exp(-delta_cost/t) > np.random.rand():
               cur_solution = new_solution.copy()
               cur_cost = new_cost
               if cur_cost < best_cost:
                   best_solution = cur_solution.copy()
                   best_cost = cur_cost
           # 降温
           t *= alpha
           if t < t_min:
               break
       return best_solution, best_cost

5. 定义计算路径长度的函数，例如：

   def get_cost(solution, dist_mat):
       cost = 0
       for i in range(len(solution)-1):
           cost += dist_mat[solution[i]][solution[i+1]]
       cost += dist_mat[solution[-1]][solution[0]]
       return cost

6. 定义生成邻居解的函数，例如：

   def get_neighbor(solution):
       i, j = np.random.choice(len(solution), 2, replace=False)
       new_solution = solution.copy()
       new_solution[i], new_solution[j] = new_solution[j], new_solution[i]
       return new_solution

7. 调用主函数求解TSP问题并画出路径图，例如：

   # 求解TSP问题
   best_solution, best_cost = tsp_sa(dist_mat, t, t_min, alpha, n_iter)
   
   # 画出路径图
   import matplotlib.pyplot as plt
   
   plt.scatter(cities[:,0], cities[:,1])
   for i in range(len(best_solution)-1):
       plt.plot([cities[best_solution[i]][0], cities[best_solution[i+1]][0]], [cities[best_solution[i]][1], cities[best_solution[i+1]][1]], 'r')
   plt.plot([cities[best_solution[-1]][0], cities[best_solution[0]][0]], [cities[best_solution[-1]][1], cities[best_solution[0]][1]], 'r')
   plt.show()

运行以上代码后，就可以得到TSP问题模拟退火算法的最优解和路径图。