蚁群算法求解旅行商问题代码

### 蚁群算法实现旅行商问题(TSP)代码示例

#### Python版本的蚁群算法解决TSP问题

import numpy as np
import matplotlib.pyplot as plt

class AntColonyOptimization:
    def __init__(self, distances, n_ants=10, n_best=20, n_iterations=1000, decay=0.95, alpha=1, beta=1):
        self.distances = distances
        self.pheromone = np.ones(self.distances.shape) / len(distances)
        self.all_inds = range(len(distances))
        self.n_ants = n_ants
        self.n_best = n_best
        self.n_iterations = n_iterations
        self.decay = decay
        self.alpha = alpha
        self.beta = beta

    def run(self):
        shortest_path = None
        all_time_shortest_path = ("placeholder", np.inf)
        for i in range(self.n_iterations):
            all_paths = self.gen_all_paths()
            self.spread_pheronome(all_paths, self.n_best)
            self.pheromone *= self.decay
            current_shortest_path = min(all_paths, key=lambda x: x[1])
            if current_shortest_path[1] < all_time_shortest_path[1]:
                all_time_shortest_path = current_shortest_path
            shortest_path = current_shortest_path
        return all_time_shortest_path

    def spread_pheronome(self, all_paths, n_best):
        sorted_paths = sorted(all_paths, key=lambda x: x[1])
        for path, dist in sorted_paths[:n_best]:
            for move in zip(path[:-1], path[1:]):
                self.pheromone[move] += 1.0 / self.distances[move]

    def gen_path_dist(self, path):
        total_dist = 0
        for ele in zip(path[:-1], path[1:]):
            total_dist += self.distances[ele]
        return total_dist

    def gen_all_paths(self):
        all_paths = []
        for i in range(self.n_ants):
            path = self.gen_path(0)
            all_paths.append((path, self.gen_path_dist(path)))
        return all_paths

    def gen_path(self, start):
        path = []
        visited = set()
        visited.add(start)
        prev = start
        for _ in range(len(self.distances) - 1):
            move = self.pick_move(self.pheromone[prev], self.distances[prev], visited)
            path.append(move)
            prev = move
            visited.add(move)
        path.append(start)
        return path

    def pick_move(self, pheromone, dist, visited):
        pheromone = np.copy(pheromone)
        pheromone[list(visited)] = 0
        row = pheromone ** self.alpha * ((1.0 / dist) ** self.beta)
        norm_row = row / row.sum()
        move = np_choice(self.all_inds, 1, p=norm_row)[0]
        return move


def main():
    city_coordinates = [
        (60, 200), (84, 253), (70, 25), (100, 100),
        (200, 160), (150, 5), (50, 50), (150, 300),
        (300, 200), (200, 100), (300, 100), (150, 75)
    ]
    
    distance_matrix = calculate_distance(city_coordinates)

    aco = AntColonyOptimization(distance_matrix, n_ants=20, n_best=20,
                                n_iterations=1000, decay=0.95, alpha=1, beta=1)
    shortest_path = aco.run()

    print(f'Shortest Path found by ACO is {shortest_path}')
    plot_tsp(shortest_path)


def calculate_distance(coordinates):
    number_of_cities = len(coordinates)
    matrix = [[0 for col in range(number_of_cities)]
              for row in range(number_of_cities)]

    for idx_from, coord_from in enumerate(coordinates):
        for idx_to, coord_to in enumerate(coordinates):
            dx, dy = coord_from[0]-coord_to[0], coord_from[1]-coord_to[1]
            dist = round(np.sqrt(dx*dx + dy*dy))  # Euclidean Distance
            matrix[idx_from][idx_to] = dist
    
    return np.array(matrix)


def plot_tsp(solution):
    cities = solution[0]
    coords = [(60, 200), (84, 253), (70, 25), (100, 100),
              (200, 160), (150, 5), (50, 50), (150, 300),
              (300, 200), (200, 100), (300, 100), (150, 75)]
              
    plt.figure(figsize=(10, 7))

    xs, ys = [], []
    for c in cities:
        xs.append(coords[c][0])
        ys.append(coords[c][1])

    xs.append(xs[0])  # Return to the starting point.
    ys.append(ys[0])

    plt.plot(xs, ys, 'o-r')
    plt.show()


if __name__ == "__main__":
    main()

此段代码展示了如何利用蚁群算法来找到给定一组城市的最短路径[^1]。通过定义`AntColonyOptimization`类，实现了蚂蚁个体的行为逻辑及其群体协作机制，并最终找到了一条较优的城市访问顺序。