大规模车辆路径问题算法及代码实现

大规模车辆路径问题是一个NP难问题，目前还没有找到一种能够在多项式时间内解决的算法。但是，有一些启发式算法可以用来近似求解该问题，例如遗传算法、模拟退火算法、禁忌搜索算法等。下面是一个使用遗传算法求解大规模车辆路径问题的Python代码示例：

import random

# 车辆路径问题的遗传算法求解
class GA_TSP:
    def __init__(self, city_num, pop_size, pc, pm, max_iter):
        self.city_num = city_num  # 城市数量
        self.pop_size = pop_size  # 种群大小
        self.pc = pc  # 交叉概率
        self.pm = pm  # 变异概率
        self.max_iter = max_iter  # 最大迭代次数
        self.city_pos = []  # 城市坐标
        self.pop = []  # 种群
        self.fitness = []  # 适应度
        self.best_path = []  # 最优路径
        self.best_fitness = float('inf')  # 最优适应度

    # 初始化种群
    def init_pop(self):
        for i in range(self.pop_size):
            path = list(range(self.city_num))
            random.shuffle(path)
            self.pop.append(path)

    # 计算适应度
    def calc_fitness(self, path):
        dist = 0
        for i in range(self.city_num - 1):
            dist += ((self.city_pos[path[i]][0] - self.city_pos[path[i+1]][0])**2 + (self.city_pos[path[i]][1] - self.city_pos[path[i+1]][1])**2)**0.5
        return 1 / dist

    # 选择操作
    def selection(self):
        new_pop = []
        for i in range(self.pop_size):
            idx1, idx2 = random.sample(range(self.pop_size), 2)
            if self.fitness[idx1] > self.fitness[idx2]:
                new_pop.append(self.pop[idx1])
            else:
                new_pop.append(self.pop[idx2])
        self.pop = new_pop

    # 交叉操作
    def crossover(self):
        for i in range(0, self.pop_size, 2):
            if random.random() < self.pc:
                idx1, idx2 = random.sample(range(self.city_num), 2)
                if idx1 > idx2:
                    idx1, idx2 = idx2, idx1
                child1, child2 = [-1] * self.city_num, [-1] * self.city_num
                for j in range(idx1, idx2+1):
                    child1[j] = self.pop[i+1][j]
                    child2[j] = self.pop[i][j]
                idx = idx2 + 1
                for j in range(self.city_num):
                    if self.pop[i][j] not in child1:
                        child1[idx] = self.pop[i][j]
                        idx = (idx + 1) % self.city_num
                    if self.pop[i+1][j] not in child2:
                        child2[idx] = self.pop[i+1][j]
                        idx = (idx + 1) % self.city_num
                self.pop[i], self.pop[i+1] = child1, child2

    # 变异操作
    def mutation(self):
        for i in range(self.pop_size):
            if random.random() < self.pm:
                idx1, idx2 = random.sample(range(self.city_num), 2)
                self.pop[i][idx1], self.pop[i][idx2] = self.pop[i][idx2], self.pop[i][idx1]

    # 迭代
    def run(self):
        self.init_pop()
        for i in range(self.max_iter):
            self.fitness = [self.calc_fitness(path) for path in self.pop]
            best_idx = self.fitness.index(max(self.fitness))
            if self.fitness[best_idx] > self.best_fitness:
                self.best_path = self.pop[best_idx]
                self.best_fitness = self.fitness[best_idx]
            self.selection()
            self.crossover()
            self.mutation()
        return self.best_path, self.best_fitness

if __name__ == '__main__':
    city_num = 20  # 城市数量
    pop_size = 100  # 种群大小
    pc = 0.8  # 交叉概率
    pm = 0.1  # 变异概率
    max_iter = 1000  # 最大迭代次数
    city_pos = [(random.random(), random.random()) for i in range(city_num)]  # 随机生成城市坐标
    ga_tsp = GA_TSP(city_num, pop_size, pc, pm, max_iter)
    ga_tsp.city_pos = city_pos
    best_path, best_fitness = ga_tsp.run()
    print('最优路径：', best_path)
    print('最优适应度：', best_fitness)