LKH算法python实现

LKH算法是一个经典的TSP问题求解算法，下面是一个简单的Python实现，仅供参考：

import random
import math

# 计算两个城市之间的距离
def distance(city1, city2):
    return math.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)

# 生成随机的城市坐标
def generate_cities(num_cities):
    cities = []
    for i in range(num_cities):
        x = random.random()
        y = random.random()
        cities.append((x, y))
    return cities

# 计算路径长度
def path_length(path, cities):
    return sum(distance(cities[path[i]], cities[path[i+1]]) for i in range(len(path)-1)) + distance(cities[path[-1]], cities[path[0]])

# 两点交换
def two_opt(path, i, j):
    return path[:i] + path[i:j+1][::-1] + path[j+1:]

# LKH算法
def lkh(num_cities, num_iterations):
    cities = generate_cities(num_cities)
    path = list(range(num_cities))
    best_path = path[:]
    best_length = path_length(best_path, cities)
    for iteration in range(num_iterations):
        for i in range(1, num_cities-1):
            for j in range(i+1, num_cities):
                new_path = two_opt(path, i, j)
                new_length = path_length(new_path, cities)
                if new_length < best_length:
                    best_path = new_path[:]
                    best_length = new_length
        path = best_path[:]
    return best_length, best_path

# 测试代码
if __name__ == '__main__':
    num_cities = 20
    num_iterations = 1000
    best_length, best_path = lkh(num_cities, num_iterations)
    print('Best length:', best_length)
    print('Best path:', best_path)

以上代码实现了LKH算法的基本思路，但是由于时间复杂度较高，对于大规模数据的求解效率较低，需要进行优化。