在python中用遗传算法求解传教士和野人渡河问题

传教士和野人渡河问题是一个经典的人工智能问题，可以用遗传算法来求解。下面是一个简单的 Python 实现：

首先，我们需要定义问题的状态和操作。在这个问题中，状态包括当前河岸上的传教士和野人数量，以及船只的位置；操作包括将传教士或野人从一个河岸移动到另一个河岸。

import random

class State:
    def __init__(self, left_m, left_c, right_m, right_c, boat):
        self.left_m = left_m # 左岸传教士数量
        self.left_c = left_c # 左岸野人数量
        self.right_m = right_m # 右岸传教士数量
        self.right_c = right_c # 右岸野人数量
        self.boat = boat # 船只位置：0 表示在左岸，1 表示在右岸

    def is_valid(self):
        if self.left_m < 0 or self.left_c < 0 or self.right_m < 0 or self.right_c < 0:
            return False
        if self.left_m > 0 and self.left_m < self.left_c:
            return False
        if self.right_m > 0 and self.right_m < self.right_c:
            return False
        return True

    def move(self, m, c):
        if self.boat == 0:
            return State(self.left_m - m, self.left_c - c, self.right_m + m, self.right_c + c, 1)
        else:
            return State(self.left_m + m, self.left_c + c, self.right_m - m, self.right_c - c, 0)

    def __str__(self):
        return f"({self.left_m}, {self.left_c}, {self.right_m}, {self.right_c}, {self.boat})"

接下来，我们需要定义遗传算法的种群和适应度函数。在这个问题中，一个个体就是一系列操作序列，我们通过随机生成一些操作序列来初始化种群。适应度函数就是求解这个操作序列所对应的最短路径长度。

POPULATION_SIZE = 100
NUM_GENERATIONS = 1000

def generate_population():
    return [[random.randint(0, 2), random.randint(0, 2)] for _ in range(POPULATION_SIZE)]

def fitness(individual):
    state = State(3, 3, 0, 0, 0)
    path_length = 0
    for action in individual:
        new_state = state.move(*action)
        if new_state.is_valid():
            state = new_state
            path_length += 1
        else:
            path_length += 10 # 惩罚非法状态
    return 1 / (path_length + 1)

最后，我们可以运行遗传算法来求解最短路径：

def evolve():
    population = generate_population()

    for generation in range(NUM_GENERATIONS):
        fitnesses = [fitness(individual) for individual in population]
        print(f"Generation {generation}: best fitness = {max(fitnesses)}")

        # 选择
        selected_indices = random.choices(range(POPULATION_SIZE), weights=fitnesses, k=POPULATION_SIZE)

        # 交叉
        offspring = []
        for i in range(0, POPULATION_SIZE, 2):
            parent1 = population[selected_indices[i]]
            parent2 = population[selected_indices[i + 1]]
            child1 = [parent1[0], parent2[1]]
            child2 = [parent2[0], parent1[1]]
            offspring.extend([child1, child2])

        # 变异
        for i in range(POPULATION_SIZE):
            if random.random() < 0.1:
                offspring[i][0] = random.randint(0, 2)
            if random.random() < 0.1:
                offspring[i][1] = random.randint(0, 2)

        population = offspring

    best_individual = max(population, key=fitness)
    print(f"Best individual: {best_individual}, fitness = {fitness(best_individual)}")

这个遗传算法的实现非常简单，可以通过增加种群大小和迭代次数来提高求解的精度。