遗传算法解决tsp问题，用Python让旅程优化

2023-04-16 15:59:03

遗传算法简介：解决TSP问题的有力工具

遗传算法：自然启发的优化

遗传算法（GA）是一种受自然选择和遗传学启发的优化算法。它通过模拟自然界的进化过程来寻找问题的最优解。遗传算法的优势在于，它不需要对问题有深入的了解，也不需要提供初始解，因此它可以应用于各种各样的优化问题。

TSP问题：旅行商的困境

TSP（Traveling Salesman Problem）问题是经典的组合优化问题之一。它了一个旅行商需要访问多个城市，并希望找到一条最短的路线来完成所有访问，最后回到出发城市。TSP问题在现实生活中有很多应用场景，例如物流配送、车辆调度和旅行规划等。

遗传算法解决TSP问题

遗传算法解决TSP问题的基本流程如下：

初始化种群： 随机生成一组候选解，每个候选解表示一条可能的旅行路线。
计算适应度： 计算每个候选解的适应度，即该路线的总距离。适应度高的候选解有更大的机会被选中。
选择： 根据适应度对候选解进行选择，适应度高的候选解更有可能被选中。
交叉： 将两个候选解进行交叉操作，产生新的候选解。交叉操作可以帮助探索新的解空间。
变异： 对新的候选解进行变异操作，即随机改变一些候选解的元素。变异操作可以帮助避免陷入局部最优解。
重复2-5步： 重复2-5步，直到满足终止条件（例如达到最大迭代次数或找到最优解）。

Python代码示例：遗传算法求解TSP

import random
import math

class TSPSolver:
    def __init__(self, cities):
        self.cities = cities
        self.num_cities = len(cities)
        self.distance_matrix = self.create_distance_matrix()

    def create_distance_matrix(self):
        distance_matrix = [[0 for _ in range(self.num_cities)] for _ in range(self.num_cities)]
        for i in range(self.num_cities):
            for j in range(self.num_cities):
                if i == j:
                    distance_matrix[i][j] = 0
                else:
                    distance_matrix[i][j] = self.calculate_distance(self.cities[i], self.cities[j])
        return distance_matrix

    def calculate_distance(self, city1, city2):
        x1, y1 = city1
        x2, y2 = city2
        return math.sqrt((x1 - x2)**2 + (y1 - y2)**  2)

    def generate_initial_population(self, population_size):
        population = []
        for _ in range(population_size):
            population.append(self.generate_random_tour())
        return population

    def generate_random_tour(self):
        tour = list(range(self.num_cities))
        random.shuffle(tour)
        return tour

    def calculate_tour_distance(self, tour):
        total_distance = 0
        for i in range(self.num_cities):
            total_distance += self.distance_matrix[tour[i]][tour[(i+1) % self.num_cities]]
        return total_distance

    def select_parents(self, population, num_parents):
        parents = []
        for _ in range(num_parents):
            parent1 = self.roulette_wheel_selection(population)
            parent2 = self.roulette_wheel_selection(population)
            parents.append((parent1, parent2))
        return parents

    def roulette_wheel_selection(self, population):
        total_fitness = sum(self.calculate_tour_distance(tour) for tour in population)
        random_value = random.uniform(0, total_fitness)
        current_fitness = 0
        for tour in population:
            current_fitness += self.calculate_tour_distance(tour)
            if current_fitness >= random_value:
                return tour
        return population[-1]

    def crossover(self, parent1, parent2):
        crossover_point = random.randint(1, self.num_cities-2)
        child1 = parent1[:crossover_point] + parent2[crossover_point:]
        child2 = parent2[:crossover_point] + parent1[crossover_point:]
        return child1, child2

    def mutate(self, tour):
        mutation_point = random.randint(0, self.num_cities-1)
        city1 = tour[mutation_point]
        city2 = tour[(mutation_point+1) % self.num_cities]
        tour[mutation_point] = city2
        tour[(mutation_point+1) % self.num_cities] = city1
        return tour

    def genetic_algorithm(self, population_size=100, num_generations=100):
        population = self.generate_initial_population(population_size)
        for generation in range(num_generations):
            parents = self.select_parents(population, num_parents=2)
            children = []
            for parent1, parent2 in parents:
                child1, child2 = self.crossover(parent1, parent2)
                child1 = self.mutate(child1)
                child2 = self.mutate(child2)
                children.append(child1)
                children.append(child2)
            population = population + children
            population = sorted(population, key=self.calculate_tour_distance)
            population = population[:population_size]
        best_tour = population[0]
        best_distance = self.calculate_tour_distance(best_tour)
        return best_tour, best_distance

if __name__ == "__main__":
    cities = [(0, 0), (10, 0), (20, 0), (30, 0), (40, 0)]
    solver = TSPSolver(cities)
    best_tour, best_distance = solver.genetic_algorithm()
    print("Best tour:", best_tour)
    print("Best distance:", best_distance)