用遗传算法求解不同规模用遗传算法求解不同规模（如10个城市，20个城市，100个城市）的TSP问题（如10个城市，20个城市，100个城市）的TSP问题，使用python语言编写代码

遗传算法是一种基于生物进化理论的优化搜索技术，适用于解决复杂问题，如旅行商问题（Traveling Salesman Problem，TSP）。对于不同规模的城市数，TSP问题的复杂度会显著增加。下面是一个简化的Python遗传算法求解TSP问题的大致步骤：

首先，需要导入必要的库：

import random
import numpy as np
from deap import base, creator, tools

创建个体和适应度函数：

creator.create("FitnessMax", base.Fitness, weights=(1.0,))
creator.create("Individual", list, fitness=creator.FitnessMax)

def distance(city_list):
    # 计算两点间的欧几里得距离或其他合适的距离计算方法
    pass

def tsp_fitness(individual):
    total_distance = sum(distance(city_list[i], city_list[j]) for i in range(len(city_list)) for j in (i+1) % len(city_list))
    return total_distance,

初始化种群、选择、交叉和变异操作：

def init_population(n, cities):
    population = [creator.Individual(random.sample(cities, cities)) for _ in range(n)]
    return population

def selection(population, toolbox, k):
    return toolbox.select(population, k)

def crossover(parents, offspring_size):
    toolbox = base.Toolbox()
    toolbox.register("mate", tools.cxTwoPoint)
    return [toolbox.mate(*parent) for parent in zip(*[iter(parents)]*2)]

def mutate(individual, mutation_rate):
    toolbox = base.Toolbox()
    toolbox.register("mutate", tools.mutShuffleIndexes, indpb=mutation_rate)
    return toolbox.mutate(list(individual))

# 主循环
def genetic_algorithm(pop_size, generations, cities, mutation_rate):
    pop = init_population(pop_size, cities)
    best_solution = None
    for g in range(generations):
        offspring = crossover(pop, int(0.5 * pop_size))
        offspring = [mutate(ind, mutation_rate) for ind in offspring]
        offspring = [toolbox.clone(ind) for ind in offspring]

        offspring = [tsp_fitness(ind)[0] if tsp_fitness(ind)[0] < (best_solution.fitness.values[0] if best_solution else float("inf")) else ind.fitness.values for ind in offspring]
        offspring.sort(key=lambda x: x.fitness.values)

        # 更新最佳解决方案
        best_solution = offspring[0] if best_solution is None or offspring[0].fitness > best_solution.fitness else best_solution
        
        pop[:] = offspring[:pop_size]

    return best_solution, pop

现在你可以根据城市数量（例如10、20或100）调用`genetic_algorithm`函数：

solution, best_path = genetic_algorithm(pop_size=100, generations=1000, cities=your_city_list, mutation_rate=0.01)