用Python编写程序如果要求先将64件物品分成四个大组,每个大组有16件物品,然后再将每个大组分成四个小组,每个小组有4件物品。要求分组后大组之间的总重量差不超过1,同时每个大组内部各小组之间的总体积差也要尽可能小。
时间: 2024-03-31 20:36:51 浏览: 16
以下是一个使用遗传算法解决该问题的Python程序示例:
``` python
import random
# 物品列表,每个物品有重量和体积两个属性
items = [{'weight': 1, 'volume': 1}, {'weight': 2, 'volume': 2}, {'weight': 3, 'volume': 3}, ...]
# 每个大组的物品数量
group_size = 16
# 每个小组的物品数量
subgroup_size = 4
# 遗传算法的相关参数
population_size = 100 # 种群大小
mutation_rate = 0.01 # 变异率
generations = 1000 # 迭代次数
# 计算每个物品的体积和重量差的函数
def calc_diff(group):
weights = [item['weight'] for item in group]
volumes = [item['volume'] for item in group]
weight_diff = max(weights) - min(weights)
volume_diff = 0
for i in range(len(volumes)):
for j in range(i+1, len(volumes)):
volume_diff += abs(volumes[i] - volumes[j])
return (weight_diff, volume_diff)
# 生成一个符合要求的分组方案
def generate_group():
group = []
for i in range(group_size):
group.append(random.choice(items))
subgroups = [[], [], [], []]
for item in group:
subgroup = random.choice(subgroups)
subgroup.append(item)
return subgroups
# 计算一个分组方案的适应度,适应度越小,说明分组效果越好
def calc_fitness(group):
weight_diffs = []
volume_diffs = []
for subgroup in group:
weight_diff, volume_diff = calc_diff(subgroup)
weight_diffs.append(weight_diff)
volume_diffs.append(volume_diff)
group_weight_diff = max(weight_diffs) - min(weight_diffs)
group_volume_diff = sum(volume_diffs)
return group_weight_diff + group_volume_diff
# 生成初始种群
population = [generate_group() for i in range(population_size)]
# 迭代遗传算法
for generation in range(generations):
# 计算每个个体的适应度
fitness_values = [calc_fitness(group) for group in population]
# 选择操作,使用轮盘赌算法
total_fitness = sum(fitness_values)
selection_probs = [fitness / total_fitness for fitness in fitness_values]
new_population = []
for i in range(population_size):
parent1 = random.choices(population, weights=selection_probs)[0]
parent2 = random.choices(population, weights=selection_probs)[0]
child = []
for subgroup1, subgroup2 in zip(parent1, parent2):
subgroup = []
for item1, item2 in zip(subgroup1, subgroup2):
if random.random() < 0.5:
subgroup.append(item1)
else:
subgroup.append(item2)
child.append(subgroup)
new_population.append(child)
# 变异操作,随机选择一个大组,对该大组进行随机交换其两个小组的操作
for i in range(population_size):
if random.random() < mutation_rate:
group = random.choice(new_population[i])
subgroup1, subgroup2 = random.sample(group, 2)
index1 = group.index(subgroup1)
index2 = group.index(subgroup2)
group[index1], group[index2] = subgroup2, subgroup1
population = new_population
# 找到适应度最小的分组方案
fitness_values = [calc_fitness(group) for group in population]
min_fitness_index = fitness_values.index(min(fitness_values))
best_group = population[min_fitness_index]
# 输出最优分组方案
for i, subgroup in enumerate(best_group):
print(f'Group {i+1}:')
for item in subgroup:
print(item)
```
需要注意的是,这个程序只是一个示例,可能需要根据具体问题进行调整。
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