遗传算法解决三维装箱问题

遗传算法是一种优化算法，可以用于解决三维装箱问题。

以下是一个基于遗传算法的简单实现：

1. 初始化一个种群，其中每个个体代表一个物品的排列顺序
2. 计算每个个体的适应度，即该排列顺序下的物品装箱效率
3. 选择一些适应度较高的个体进行交叉和变异操作，生成下一代种群
4. 重复步骤2-3，直到达到最大迭代次数或找到一个满意的解决方案
5. 输出最优解决方案

具体实现可以参考以下的Python代码实现：

import random

class Box:
    def __init__(self, width, height, depth):
        self.width = width
        self.height = height
        self.depth = depth
        self.items = []

    def add_item(self, item):
        self.items.append(item)

    def get_volume(self):
        return self.width * self.height * self.depth

class Item:
    def __init__(self, id, width, height, depth):
        self.id = id
        self.width = width
        self.height = height
        self.depth = depth
        self.volume = width * height * depth

def pack_items(items, container):
    for item in items:
        fit_box = None
        for box in container:
            if box.width >= item.width and box.height >= item.height and box.depth >= item.depth:
                if fit_box is None or box.get_volume() < fit_box.get_volume():
                    fit_box = box
        if fit_box is not None:
            fit_box.add_item(item)
        else:
            return False
    return True

def generate_individual(items):
    return random.sample(items, len(items))

def generate_population(items, population_size):
    return [generate_individual(items) for i in range(population_size)]

def calculate_fitness(individual, container):
    items = [Item(i, item[0], item[1], item[2]) for i, item in enumerate(individual)]
    if pack_items(items, container):
        total_volume = sum([box.get_volume() for box in container])
        return 1 / total_volume
    else:
        return 0

def crossover(individual1, individual2):
    n = len(individual1)
    c = random.randint(0, n-1)
    return individual1[:c] + individual2[c:], individual2[:c] + individual1[c:]

def mutate(individual, items):
    n = len(individual)
    i, j = random.sample(range(n), 2)
    individual[i], individual[j] = individual[j], individual[i]
    while True:
        k = random.randint(0, n-1)
        if k != i and k != j:
            break
    individual[k] = random.choice(items)
    return individual

def select_population(population, fitness, n):
    return [population[i] for i in sorted(random.sample(range(len(population)), n), key=lambda i: fitness[i], reverse=True)]

def genetic_algorithm(items, container, population_size, elite_size, mutation_rate, generations):
    population = generate_population(items, population_size)
    for i in range(generations):
        fitness = [calculate_fitness(individual, container) for individual in population]
        elites = select_population(population, fitness, elite_size)
        next_generation = elites
        while len(next_generation) < population_size:
            if random.random() < mutation_rate:
                parent = random.choice(elites)
                child = mutate(parent[:], items)
            else:
                parent1, parent2 = random.sample(elites, 2)
                child1, child2 = crossover(parent1[:], parent2[:])
                child = child1 if calculate_fitness(child1, container) > calculate_fitness(child2, container) else child2
            next_generation.append(child)
        population = next_generation
    fitness = [calculate_fitness(individual, container) for individual in population]
    best_individual = population[fitness.index(max(fitness))]
    return best_individual

# Example usage
items = [(20, 30, 40), (15, 25, 35), (10, 20, 30), (5, 10, 15)]
container = [Box(100, 100, 100)]
best_individual = genetic_algorithm(items, container, population_size=50, elite_size=10, mutation_rate=0.1, generations=100)
best_items = [Item(i, item[0], item[1], item[2]) for i, item in enumerate(best_individual)]
pack_items(best_items, container)

for i, box in enumerate(container):
    print(f"Box {i+1}:")
    for item in box.items:
        print(f"  Item {item.id}: ({item.width}, {item.height}, {item.depth})")

这段代码使用了遗传算法来解决三维装箱问题。首先，使用`generate_population`函数生成一个种群，其中每个个体代表一个物品的排列顺序。然后，使用`calculate_fitness`函数计算每个个体的适应度，即该排列顺序下的物品装箱效率。接下来，使用`select_population`函数选择一些适应度较高的个体进行交叉和变异操作，生成下一代种群。最后，重复上述步骤，直到达到最大迭代次数或找到一个满意的解决方案。在每次迭代中，使用`mutation_rate`参数控制个体发生变异的概率，使用`elite_size`参数控制选择适应度较高的个体数量。