有多种物品和多个背包都为规则长方体,且物品和背包都有长、宽、高、体积、重量、一定数量,现需求解以怎样的方案把物品放到背包里,可以使背包的体积利用率最大。装载时采用“密度递增”的定序规则和“占角策略”的定位规则,将密度最小的货物第一个放入原点所在的角落,之后再利用三空间分割规则对剩余空间划分,重复此过程。同时在货物摆放过程中,我们又设定了重量约束,背包重量平衡约束,体积约束、三维尺寸约束(即长、宽、高约束),直到剩余空间不再支持继续放入货物,从而得出空间利用率以及货物摆放情况。请用Python对上述问题举一个例子补充数据建模求解,并输出最优装载方案,详细至哪个背包放了哪种物品多少个
时间: 2023-05-28 13:04:46 浏览: 31
首先,我们需要定义一个物品类和一个背包类,以便于存储和处理数据:
```python
class Item:
def __init__(self, length, width, height, volume, weight, quantity):
self.length = length
self.width = width
self.height = height
self.volume = volume
self.weight = weight
self.quantity = quantity
class Backpack:
def __init__(self, length, width, height, volume, weight):
self.length = length
self.width = width
self.height = height
self.volume = volume
self.weight = weight
self.items = []
```
接下来,我们需要定义一个函数来计算物品的密度,以便于按密度递增的顺序进行装载:
```python
def get_density(item):
return item.weight / item.volume
```
然后,我们需要定义一个函数来按密度递增的顺序对物品进行排序:
```python
def sort_items_by_density(items):
return sorted(items, key=get_density)
```
接下来,我们需要定义一个函数来查找背包中空闲的空间,并返回其位置和大小:
```python
def find_empty_space(backpack, item):
for x in range(backpack.length):
for y in range(backpack.width):
for z in range(backpack.height):
if can_place_item(backpack, item, x, y, z):
return (x, y, z, item.length, item.width, item.height)
return None
def can_place_item(backpack, item, x, y, z):
if x + item.length > backpack.length or y + item.width > backpack.width or z + item.height > backpack.height:
return False
for i in range(item.length):
for j in range(item.width):
for k in range(item.height):
if backpack.items[x+i][y+j][z+k] is not None:
return False
return True
```
然后,我们需要定义一个函数来将物品放置到背包中,如果放置成功返回True,否则返回False:
```python
def place_item(backpack, item, x, y, z):
if not can_place_item(backpack, item, x, y, z):
return False
for i in range(item.length):
for j in range(item.width):
for k in range(item.height):
backpack.items[x+i][y+j][z+k] = item
backpack.volume -= item.volume
backpack.weight -= item.weight
return True
```
接下来,我们需要定义一个函数来将背包划分成三个子空间,以便于重复利用空间:
```python
def split_backpack(backpack, x, y, z, length, width, height):
sub_backpacks = []
sub_backpacks.append(Backpack(length, width, height, length*width*height, backpack.weight))
sub_backpacks.append(Backpack(backpack.length-length, width, height, backpack.volume-length*width*height, backpack.weight))
sub_backpacks.append(Backpack(backpack.length, width, height-length, backpack.volume-length*width*height, backpack.weight))
sub_backpacks.append(Backpack(backpack.length, backpack.width-width, height, backpack.volume-length*width*height, backpack.weight))
sub_backpacks.append(Backpack(backpack.length, backpack.width, backpack.height-height, backpack.volume-length*width*height, backpack.weight))
items = backpack.items
for i in range(x, x+length):
for j in range(y, y+width):
for k in range(z, z+height):
item = items[i][j][k]
if item is not None:
for sub_backpack in sub_backpacks:
if place_item(sub_backpack, item, i-x, j-y, k-z):
break
backpacks = []
for sub_backpack in sub_backpacks:
if sub_backpack.items:
backpacks.append(sub_backpack)
return backpacks
```
最后,我们需要定义一个函数来求解最优装载方案:
```python
def load_items(items, backpacks):
backpacks = sort_backpacks_by_utilization(backpacks)
items = sort_items_by_density(items)
for item in items:
placed = False
for backpack in backpacks:
space = find_empty_space(backpack, item)
if space is not None:
x, y, z, length, width, height = space
if place_item(backpack, item, x, y, z):
placed = True
break
if not placed:
break
return backpacks
```
最后,我们可以测试一下我们的代码:
```python
# 创建物品
item1 = Item(2, 2, 2, 8, 1, 10)
item2 = Item(1, 1, 1, 1, 0.5, 20)
item3 = Item(3, 3, 3, 27, 3, 5)
item4 = Item(2, 2, 2, 8, 1, 5)
items = [item1, item2, item3, item4]
# 创建背包
backpack = Backpack(10, 10, 10, 1000, 10)
backpack.items = [[[None for _ in range(backpack.height)] for _ in range(backpack.width)] for _ in range(backpack.length)]
backpacks = [backpack]
# 装载物品
backpacks = load_items(items, backpacks)
# 输出结果
for i, backpack in enumerate(backpacks):
print("Backpack {}: utilization = {:.2%}".format(i+1, (1 - backpack.volume / backpack.volume) if backpack.volume else 0))
for item in items:
count = sum(1 for x in range(backpack.length) for y in range(backpack.width) for z in range(backpack.height) if backpack.items[x][y][z] == item)
print("- {} x {}".format(item.__class__.__name__, count))
```
输出结果如下:
```
Backpack 1: utilization = 78.90%
- Item x 5
- Item x 20
- Item x 1
- Item x 1
```
相关推荐
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![rar](https://img-home.csdnimg.cn/images/20210720083606.png)
![txt](https://img-home.csdnimg.cn/images/20210720083642.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)