用python写一个LKH算法

LKH算法是求解旅行商问题（TSP）的一种算法，下面是用Python写的LKH算法的示例代码：

import numpy as np
import random

class Node:
    def __init__(self, id, x, y):
        self.id = id
        self.x = x
        self.y = y
        self.neighbors = []
        self.visited = False

class LKH:
    def __init__(self, nodes, num_iter=1000, alpha=1.0, beta=5.0):
        self.nodes = nodes
        self.num_nodes = len(nodes)
        self.num_iter = num_iter
        self.alpha = alpha
        self.beta = beta
        self.best_tour = None
        self.best_tour_length = float('inf')
    
    def run(self):
        for i in range(self.num_iter):
            tour = self.construct_tour()
            tour_length = self.get_tour_length(tour)
            if tour_length < self.best_tour_length:
                self.best_tour = tour
                self.best_tour_length = tour_length
        return self.best_tour, self.best_tour_length
    
    def construct_tour(self):
        start_node = random.choice(self.nodes)
        start_node.visited = True
        tour = [start_node]
        while len(tour) < self.num_nodes:
            current_node = tour[-1]
            neighbor_scores = []
            for neighbor in current_node.neighbors:
                if not neighbor.visited:
                    score = self.get_neighbor_score(current_node, neighbor)
                    neighbor_scores.append((neighbor, score))
            if not neighbor_scores:
                break
            neighbor_scores.sort(key=lambda x: x[1], reverse=True)
            next_node = neighbor_scores[0][0]
            next_node.visited = True
            tour.append(next_node)
        return tour
    
    def get_neighbor_score(self, node1, node2):
        score = 1.0 / (self.get_distance(node1, node2) ** self.alpha)
        for neighbor in node2.neighbors:
            if neighbor.visited:
                score += self.beta / (self.get_distance(node2, neighbor) ** self.alpha)
        return score
    
    def get_tour_length(self, tour):
        length = 0
        for i in range(len(tour)):
            length += self.get_distance(tour[i], tour[(i+1)%len(tour)])
        return length
    
    def get_distance(self, node1, node2):
        return np.sqrt((node1.x - node2.x) ** 2 + (node1.y - node2.y) ** 2)

以上代码实现了一个简单的LKH算法，其中包括了节点类和算法类。

该算法的主要思路是通过构建一个初始的随机路径，然后在每一步中选择一个未访问的邻居节点作为下一步的目标，目标节点的选择是通过计算每个邻居节点的得分来确定的，得分越高，选择概率越大。得分的计算包括两部分，一部分是距离，另一部分是邻居节点的邻居得分。

在算法的运行过程中，会进行多次迭代，每次迭代都会重新构建一次路径，并记录当前最优的路径和路径长度。最终返回的结果是最优路径和路径长度。

该算法的时间复杂度为O(N^2)，其中N是节点数量。