本关任务：编写一个爬山算法的小程序，通过局部搜索输出邻域范围内的最优解。

好的，下面是一个简单的 Python 实现，用于解决 TSP（Traveling Salesman Problem，旅行商问题）：

import random
import math

# 城市坐标
cities = [(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), (20, 20), (60, 20), (160, 20)]

# 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)

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

# 随机生成一个初始解
def init_solution(n):
    return list(range(n))

# 对当前解进行邻域搜索
def neighborhood(solution):
    neighborhoods = []
    for i in range(len(solution)):
        for j in range(i+1, len(solution)):
            neighbor = solution.copy()
            neighbor[i], neighbor[j] = neighbor[j], neighbor[i]
            neighborhoods.append(neighbor)
    return neighborhoods

# 爬山算法
def hill_climbing():
    # 初始化
    current_solution = init_solution(len(cities))
    current_length = path_len(current_solution)
    print("Initial solution:", current_solution)
    print("Initial length:", current_length)
    
    # 迭代搜索
    while True:
        neighbors = neighborhood(current_solution)
        neighbors_lengths = [(path_len(neighbor), neighbor) for neighbor in neighbors]
        neighbors_lengths.sort()
        if neighbors_lengths[0][0] >= current_length:
            # 搜索结束，找到最优解
            break
        current_length, current_solution = neighbors_lengths[0]
        print("Current solution:", current_solution)
        print("Current length:", current_length)
    
    # 输出最优解
    print("Best solution found:", current_solution)
    print("Best length found:", current_length)

if __name__ == '__main__':
    hill_climbing()

这段代码会随机生成一个初始解，然后进行邻域搜索，每次选择路径长度更短的解作为当前解，直到找到最优解或达到最大迭代次数。最后输出最优解及其路径长度。