利用蚁群算法编写求解多目标多旅行商问题的代码

以下是利用蚁群算法求解多目标多旅行商问题的Python代码，其中采用了NSGA-II算法对多个目标进行优化：

import numpy as np
import random
import copy

class Ant:
    def __init__(self, num_cities):
        self.num_cities = num_cities
        self.visited_cities = []
        self.distance = 0.0
        self.pheromone_delta = np.zeros((num_cities, num_cities))

    def visit_city(self, city_index, distance):
        self.visited_cities.append(city_index)
        self.distance += distance

    def update_pheromone_delta(self):
        for i in range(self.num_cities - 1):
            from_city = self.visited_cities[i]
            to_city = self.visited_cities[i+1]
            self.pheromone_delta[from_city][to_city] += 1.0 / self.distance

    def clear(self):
        self.visited_cities = []
        self.distance = 0.0
        self.pheromone_delta = np.zeros((self.num_cities, self.num_cities))

def init_pheromone(num_cities, init_pheromone_value=0.1):
    return np.ones((num_cities, num_cities)) * init_pheromone_value

def prob(city_i, city_j, pheromone, dist, alpha, beta):
    return (pheromone[city_i][city_j] ** alpha) * ((1.0 / dist[city_i][city_j]) ** beta)

def select_city(from_city, to_city, pheromone, dist, alpha, beta):
    num_cities = pheromone.shape[0]
    prob_list = np.zeros(num_cities)
    for i in range(num_cities):
        if i == from_city:
            prob_list[i] = 0.0
        elif i in to_city:
            prob_list[i] = 0.0
        else:
            prob_list[i] = prob(from_city, i, pheromone, dist, alpha, beta)
    selected_city = np.argmax(prob_list)
    return selected_city

def select_next_city(ant, pheromone, dist, alpha, beta):
    current_city = ant.visited_cities[-1]
    available_cities = list(range(ant.num_cities))
    to_city = ant.visited_cities[:-1]
    available_cities = [i for i in available_cities if i not in to_city]
    if len(available_cities) == 0:
        return None
    next_city = select_city(current_city, available_cities, pheromone, dist, alpha, beta)
    return next_city

def simulate_ant(num_cities, pheromone, dist, alpha, beta):
    ant = Ant(num_cities)
    ant.clear()
    ant.visit_city(random.randint(0, num_cities-1), 0.0)
    for i in range(num_cities - 1):
        next_city = select_next_city(ant, pheromone, dist, alpha, beta)
        if next_city is None:
            return ant
        distance = dist[ant.visited_cities[-1]][next_city]
        ant.visit_city(next_city, distance)
    ant.visit_city(ant.visited_cities[0], dist[ant.visited_cities[-1]][ant.visited_cities[0]])
    ant.update_pheromone_delta()
    return ant

def simulate_ants(num_ants, num_cities, pheromone, dist, alpha, beta):
    ants = []
    for i in range(num_ants):
        ant = simulate_ant(num_cities, pheromone, dist, alpha, beta)
        ants.append(ant)
    return ants

def update_pheromone(pheromone, ants):
    decay_rate = 0.1
    pheromone *= (1.0 - decay_rate)
    for ant in ants:
        pheromone += ant.pheromone_delta

def sort_by_objective_values(values_list):
    num_objs = len(values_list[0])
    num_samples = len(values_list)
    sorted_samples_list = [[] for _ in range(num_objs)]
    for i in range(num_objs):
        samples_list = [(j, values_list[j][i]) for j in range(num_samples)]
        samples_list.sort(key=lambda x:x[1])
        for j in range(num_samples):
            sorted_samples_list[i].append(samples_list[j][0])
    sorted_samples = []
    for i in range(num_samples):
        sample = []
        for j in range(num_objs):
            sample.append(sorted_samples_list[j][i])
        sorted_samples.append(sample)
    return sorted_samples

def crowding_distance(values_list, sorted_samples):
    num_objs = len(values_list[0])
    num_samples = len(values_list)
    distance_list = [0.0 for _ in range(num_samples)]
    for i in range(num_objs):
        sorted_samples_obj = [(j, values_list[j][i]) for j in sorted_samples]
        sorted_samples_obj.sort(key=lambda x:x[1])
        distance_list[sorted_samples_obj[0][0]] += float('inf')
        distance_list[sorted_samples_obj[-1][0]] += float('inf')
        for j in range(1, num_samples-1):
            distance_list[sorted_samples_obj[j][0]] += (sorted_samples_obj[j+1][1] - sorted_samples_obj[j-1][1]) / (sorted_samples_obj[-1][1] - sorted_samples_obj[0][1])
    return distance_list

def nsga2(num_ants, num_cities, num_generations, dist, alpha, beta, num_objs=2):
    pheromone = init_pheromone(num_cities)
    population = []
    for i in range(num_ants):
        ant = simulate_ant(num_cities, pheromone, dist, alpha, beta)
        population.append(ant.visited_cities)
    for generation in range(num_generations):
        values_list = []
        for i in range(num_ants):
            values = []
            values.append(sum([dist[population[i][j]][population[i][(j+1)%num_cities]] for j in range(num_cities)]))
            values.append(len(set(population[i])))
            values_list.append(values)
        sorted_samples = sort_by_objective_values(values_list)
        distance_list = crowding_distance(values_list, sorted_samples)
        new_population = []
        for i in range(num_ants):
            parent1_index = random.choice(sorted_samples[:num_ants//2])
            parent2_index = random.choice(sorted_samples[:num_ants//2])
            offspring = []
            for j in range(num_cities):
                if random.random() < 0.5:
                    offspring.append(population[parent1_index][j])
                else:
                    offspring.append(population[parent2_index][j])
            new_population.append(offspring)
        population = new_population
        for i in range(num_ants):
            ant = Ant(num_cities)
            ant.visited_cities = copy.deepcopy(population[i])
            ant.distance = values_list[i][0]
            ant.update_pheromone_delta()
            simulate_ant(num_cities, pheromone, dist, alpha, beta)
            population[i] = ant.visited_cities
        update_pheromone(pheromone, ants)
    return sorted_samples

if __name__ == '__main__':
    num_cities = 10
    num_ants = 20
    num_generations = 100
    alpha = 1.0
    beta = 2.0
    dist = np.random.rand(num_cities, num_cities)
    dist += dist.T
    np.fill_diagonal(dist, 0.0)
    sorted_samples = nsga2(num_ants, num_cities, num_generations, dist, alpha, beta)
    print(sorted_samples)

在上述代码中，Ant类代表一只蚂蚁，其中visited_cities属性表示已经访问过的城市列表，distance属性表示蚂蚁已经走过的距离，pheromone_delta属性表示蚂蚁走过路径上的信息素增量。init_pheromone()函数用于初始化信息素矩阵，prob()函数用于计算从一个城市到另一个城市的转移概率，select_city()函数用于选择下一个访问的城市，simulate_ant()函数用于模拟一只蚂蚁的行为，simulate_ants()函数用于模拟多只蚂蚁的行为，update_pheromone()函数用于更新信息素矩阵。除此之外，还定义了其他一些辅助函数，如select_next_city()、sort_by_objective_values()和crowding_distance()。最后，nsga2()函数集成了多个函数，实现了多目标多旅行商问题的求解过程。