spyder基于蚁群算法求解全球所有国家首都的TSP问题并用Cartopy库画出相应地图

为了求解全球所有国家首都的 TSP 问题，可以使用 Python 的蚁群算法库 Ant Colony Optimization (ACO)。以下是实现步骤：

1. 安装 ACO 库和相关依赖库：

pip install ant-colony
pip install pandas
pip install numpy
pip install cartopy

2. 导入所需库：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
from cartopy.io.shapereader import Reader
from cartopy.feature import ShapelyFeature
from ant_colony import AntColony

3. 读取国家数据：

url = "https://raw.githubusercontent.com/datasets/country-codes/master/data/country-codes.csv"
countries = pd.read_csv(url)
capitals = countries[countries['Capital'].notna()]

4. 计算城市之间的距离矩阵：

def distance(lat1, lon1, lat2, lon2):
    R = 6371  # 地球平均半径，单位为公里
    d_lat = np.radians(lat2 - lat1)
    d_lon = np.radians(lon2 - lon1)
    lat1 = np.radians(lat1)
    lat2 = np.radians(lat2)
    a = np.sin(d_lat / 2) ** 2 + np.cos(lat1) * np.cos(lat2) * np.sin(d_lon / 2) ** 2
    c = 2 * np.arctan2(np.sqrt(a), np.sqrt(1 - a))
    distance = R * c
    return distance

n = len(capitals)
distances = np.zeros((n, n))
for i in range(n):
    for j in range(n):
        distances[i, j] = distance(capitals.iloc[i]['Latitude'], capitals.iloc[i]['Longitude'],
                                    capitals.iloc[j]['Latitude'], capitals.iloc[j]['Longitude'])

5. 创建蚁群算法对象，设置参数：

colony = AntColony(distances, n_ants=10, n_best=5, n_iterations=500, decay=0.1, alpha=1.0, beta=2.0)

6. 运行蚁群算法：

shortest_path, cost = colony.run()

7. 将城市坐标转换为地图上的坐标，绘制地图：

fig = plt.figure(figsize=(16, 12))
ax = plt.axes(projection=ccrs.PlateCarree())
ax.set_extent([-180, 180, -60, 90], crs=ccrs.PlateCarree())
ax.stock_img()
ax.add_feature(ShapelyFeature(Reader('admin_0_countries.shp').geometries(),
                              ccrs.PlateCarree(), facecolor='none', edgecolor='gray'))
for i in range(n):
    plt.plot(capitals.iloc[i]['Longitude'], capitals.iloc[i]['Latitude'], 'bo', markersize=5, transform=ccrs.Geodetic())
for i in range(n - 1):
    plt.plot([capitals.iloc[shortest_path[i]]['Longitude'], capitals.iloc[shortest_path[i+1]]['Longitude']],
             [capitals.iloc[shortest_path[i]]['Latitude'], capitals.iloc[shortest_path[i+1]]['Latitude']],
             'r-', linewidth=1, transform=ccrs.Geodetic())
plt.plot([capitals.iloc[shortest_path[0]]['Longitude'], capitals.iloc[shortest_path[-1]]['Longitude']],
         [capitals.iloc[shortest_path[0]]['Latitude'], capitals.iloc[shortest_path[-1]]['Latitude']],
         'r-', linewidth=1, transform=ccrs.Geodetic())
plt.show()

绘制出来的地图上，蓝色的点表示所有国家的首都，红线表示蚁群算法求解出的最短路径。