本文考虑了一个事实：
在某些情况下，我们在摆放物品时，总是优先选择较低的平面，基于这个常识，本文提出一种基于平面选择的三维装箱算法。
“平面”指可用于摆放货物的面。初始平面就是箱的整个底面，放入第一批货物后，“平面”包括了同批货物顶面形成的面和箱底面空余的部分。
本文算法采用由底向上的方式完成物品的装载，既优先铺满底面，然后再向上堆放物品。大体过程是：首先由完全相同的货物组成“块”，然后用块自底向上依次填充所选择的目标平面，并重新生成若干新的平面，然后不断重复上述过程来完成最终的摆放方案。下图演示了一个用4个“块”进行填充的简单过程，每个块顶部都生成了一个的平面。在这个例子中，填充完毕后，从原先的1个平面，分成了8个新的平面。
⭐️ 选择平面
当所用容器仅有一个时，初始情况下只有一个备选平面，即箱底面。
选择装载目标平面时，按照以下几条准则依次进行判断：
1) 为避免堆积过高，影响货物堆放的稳定性，优先选择空间位置较低(即参考点z坐标较小)的平面；
2) 若几个平面参考点z坐标相同，则优先选择面积较小的平面，因为面积小的平面在后面可能更难使用；
3) 若这些平面的参考点z坐标与面积均相同，则优先选择相对较狭长的平面，同样因为狭长的平面在后面可能更加难以利用；
4) 若以上3点均相同，先比较它们参考点的x坐标，选择x坐标最小的一个。若x坐标相同，则选择y坐标最小的一个。
⭐️ 填充平面
为能够充分利用空间，物品块与目标平面组合的保留规则依次为：
1) 货物组成的“块”能最大限度地利用目标平面，即放入块后目标平面剩余面积最小；
2) 若剩余面积相同，比较块的体积，保留最大体积的块。
下文将该准则简称为准则。
⭐️ 合并平面
当所选择的平面不能容纳任何一个货物时，更有效地利用空间，需进行平面合并。一个平面只能和其相邻的平面合并，相邻平面指高度相同，即具有相同参考点z坐标，至少有一边平齐，如下图所示类似情况的平面(图中蓝色部分表示目标平面(gs)，白色部分表示其相邻平面(ns))：
首先目标平面(gs)先后在平面列表和备用平面列表中依次顺序查找是否有相邻平面(ns)。平面列表指还未使用的新平面列表，备用平面列表指已经过计算不可能放入任何物品的平面的列表。当一个目标平面找到与其相邻的平面时，通过试合并决定是否保留这一合并，并进行正式合并。保留某次试合并的基本准则包括：
(1) 可以装入至少一个仍有剩余的物品(种类、方向不限)；
(2) 合并后新平面的面积是否比原先两个平面都大。
设试合并后新生产的两块平面分别为ms1和 ms2，判断是否保留该次试合并及正式合并的步骤为：
判断 ns 是否满足准则(1)。若不满足则执行第 2)步，若满足执行第 3)步；
判断 ms1 和 ms2 是否满足准则(1)。将满足的一个平面插入平面列表，不满足的放入备用平面列表。若均不满足准则(1)，则判断 ms1 和 ms2 中是否有能够足准则(2)的，若有，则将ms1和ms2均放入备用平面列表；否则不保留此次试合并，重新开始寻找相邻平面；
计算在放入物品后gs和ns将浪费的总面积(ws1)。根据ms1和ms2满足准则(1)的情况，计算合并后可能浪费的面积之和(ws2)。设平面 xs 的面积为Sqr(xs)，在该平面上放入物品后将浪费的面积为WsSqr(xs)，则根据ms1和ms2的满足准则(1)的情况，ws2有以下几种情况：
若ws1>ws2，则执行平面合并程序，并更新平面和备用平面列表；若ws1<=ws2，则不保留此次试合并，继续寻找其他相邻平面；
若对平面列表和备用平面列表搜索完毕侯，最终仍没有找到可合并的平面，则将目标平面gs从平面列表移入备用平面列表。
⭐️ 产生新平面
在放入一“块”后，原目标平面被分成3个子平面，一个位于块的顶部(下图中深色部分)，另外两个可有下面两种方式(下图中Rsa1和Rsa2)。我们选择产生的子平面面积较大的一个方式，即比较两种方式中面积较大的两个子平面，选择有最大面积子平面的生成方式。以下图为例，若(a)Rsa1>Rsa2，(b)Rsb2>Rsb1，则比较 Rsa1与Rsb2，若Rsa1>Rsb2，选择(a)方式。产生的子平面放入平面列表中。
⭐️ 程序及运行结果（笔者python运行环境为python3.7）
import copy
import sys
from itertools import product
import math
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import numpy as np
MAX_GAP = 0
# 绘图相关函数
def plot_linear_cube(ax, x, y, z, dx, dy, dz, color='red', linestyle=None):
xx = [x, x, x+dx, x+dx, x]
yy = [y, y+dy, y+dy, y, y]
kwargs = {"alpha": 1, "color": color, "linewidth":2.5, "zorder":2}
if linestyle:
kwargs["linestyle"] = linestyle
ax.plot3D(xx, yy, [z]*5, **kwargs)
ax.plot3D(xx, yy, [z+dz]*5, **kwargs)
ax.plot3D([x, x], [y, y], [z, z+dz], **kwargs)
ax.plot3D([x, x], [y+dy, y+dy], [z, z+dz], **kwargs)
ax.plot3D([x+dx, x+dx], [y+dy, y+dy], [z, z+dz], **kwargs)
ax.plot3D([x+dx, x+dx], [y, y], [z, z+dz], **kwargs)
def cuboid_data(o, size=(1, 1, 1)):
X = [[[0, 1, 0], [0, 0, 0], [1, 0, 0], [1, 1, 0]],
[[0, 0, 0], [0, 0, 1], [1, 0, 1], [1, 0, 0]],
[[1, 0, 1], [1, 0, 0], [1, 1, 0], [1, 1, 1]],
[[0, 0, 1], [0, 0, 0], [0, 1, 0], [0, 1, 1]],
[[0, 1, 0], [0, 1, 1], [1, 1, 1], [1, 1, 0]],
[[0, 1, 1], [0, 0, 1], [1, 0, 1], [1, 1, 1]]]
X = np.array(X).astype(float)
for i in range(3):
X[:, :, i] *= size[i]
X += np.array(o)
return X
def plotCubeAt(positions, sizes=None, colors=None, **kwargs):
if not isinstance(colors, (list, np.ndarray)):
colors = ["C0"] * len(positions)
if not isinstance(sizes, (list, np.ndarray)):
sizes = [(1, 1, 1)] * len(positions)
g = []
for p, s, c in zip(positions, sizes, colors):
g.append(cuboid_data(p, size=s))
return Poly3DCollection(np.concatenate(g), facecolors=np.repeat(colors, 6), **kwargs)
# 箱子类
class Box:
def __init__(self, lx, ly, lz, weight=0.0, type=0):
# 长
self.lx = lx
# 宽
self.ly = ly
# 高
self.lz = lz
# 重
self.weight = weight
# 类型
self.type = type
def __str__(self):
return "lx: {}, ly: {}, lz: {}, weight: {}, type: {}".format(self.lx, self.ly, self.lz, self.weight, self.type)
# 块类
class Block:
def __init__(self, lx, ly, lz, require_list=[], weight=0.0, box_rotate=False):
# 长
self.lx = lx
# 宽
self.ly = ly
# 高
self.lz = lz
# 需要的物品数量
self.require_list = require_list
# 需要的物品重量
self.weight = weight
# 体积
self.volume = 0
# 是否旋转
self.box_rotate = box_rotate
def __str__(self):
return "lx: %s, ly: %s, lz: %s, volume: %s, require: %s, weight: %s, box_rotate: %a" % (self.lx, self.ly, self.lz, self.volume, self.require_list, self.weight, self.box_rotate)
def __eq__(self, other):
return self.lx == other.lx and self.ly == other.ly and self.lz == other.lz and self.box_rotate == other.box_rotate and (np.array(self.require_list) == np.array(other.require_list)).all()
# 平面类
class Plane:
def __init__(self, x, y, z, lx, ly, height_limit=0):
# 坐标
self.x = x
self.y = y
self.z = z
# 长
self.lx = lx
# 宽
self.ly = ly
# 限高
self.height_limit = height_limit
self.origin = None
def __str__(self):
return "x:{}, y:{}, z:{}, lx:{}, ly:{}, height_limit:{}".format(self.x, self.y, self.z, self.lx, self.ly, self.height_limit)
def __eq__(self, other):
return self.x == other.x and self.y == other.y and self.z == other.z and self.lx == other.lx and self.ly == other.ly
# 判断是否与另一个平面相邻（z坐标相同，至少有一个边平齐），并返回合并后的两个平面
def adjacent_with(self, other):
if self.z != other.z:
return False, None, None
# 矩形中心
my_center = (self.x + self.lx / 2, self.y + self.ly / 2)
other_center = (other.x + other.lx / 2, other.y + other.ly / 2)
# 矩形相邻时的中心距离
x_adjacent_measure = self.lx / 2 + other.lx / 2
y_adjacent_measure = self.ly / 2 + other.ly / 2
# 宽边相邻，长边对齐
if x_adjacent_measure + MAX_GAP >= math.fabs(my_center[0] - other_center[0]) >= x_adjacent_measure:
if self.y == other.y and self.ly == other.ly:
ms1 = Plane(min(self.x, other.x), self.y, self.z, self.lx + other.lx, self.ly)
return True, ms1, None
if self.y == other.y:
ms1 = Plane(min(self.x, other.x), self.y, self.z, self.lx + other.lx, min(self.ly, other.ly))
if self.ly > other.ly:
ms2 = Plane(self.x, self.y + other.ly, self.z, self.lx, self.ly - other.ly)
else:
ms2 = Plane(other.x, self.y + self.ly, self.z, other.lx, other.ly - self.ly)
return True, ms1, ms2
if self.y + self.ly == other.y + other.ly:
ms1 = Plane(min(self.x, other.x), max(self.y, other.y), self.z, self.lx + other.lx, min(self.ly, other.ly))
if self.ly > other.ly:
ms2 = Plane(self.x, self.y, self.z, self.lx, self.ly - other.ly)
else:
ms2 = Plane(other.x, other.y, self.z, other.lx, other.ly - self.ly)
return True, ms1, ms2
# 长边相邻，宽边对齐
if y_adjacent_measure + MAX_GAP >= math.fabs(my_center[1] - other_center[1]) >= y_adjacent_measure:
if self.x == other.x and self.lx == other.lx:
ms1 = Plane(self.x, min(self.y, other.y), self.z, self.lx, self.ly + other.ly)
return True, ms1, None
if self.x == other.x:
ms1 = Plane(self.x, min(self.y, other.y), self.z, min(self.lx, other.lx), self.ly + other.ly)
if self.lx > other.lx:
ms2 = Plane(self.x + other.lx, self.y, self.z, self.lx - other.lx, self.ly)
else:
ms2 = Plane(self.x + self.lx, other.y, self.z, other.lx - self.lx, other.ly)
return True, ms1, ms2
if self.x + self.lx == other.x + other.lx:
ms1 = Plane(max(self.x, other.x), min(self.y, other.y), self.z, min(self.lx, other.lx), self.ly + other.ly)
if self.lx > other.lx:
ms2 = Plane(self.x, self.y, self.z, self.lx - other.lx, self.ly)
else:
ms2 = Plane(other.x, other.y, self.z, other.lx - self.lx, other.ly)
return True, ms1, ms2
return False, None, None
# 问题类
class Problem:
def __init__(self, container: Plane, height_limit=sys.maxsize, weight_limit=sys.maxsize, box_list=[], num_list=[], rotate=False):
# 初始最低水平面
self.container = container
# 限高
self.height_limit = height_limit
# 限重
self.weight_limit = weight_limit
# 箱体列表
self.box_list = box_list
# 箱体数量
self.num_list = num_list
# 是否考虑板材旋转
self.rotate = rotate
# 放置类
class Place:
def __init__(self, plane: Plane, block: Block):
self.plane = plane
self.block = block
def __eq__(self, other):
return self.plane == other.plane and self.block == other.block
# 装箱状态类
class PackingState:
def __init__(self, plane_list=[], avail_list=[], weight=0.0):
# 装箱计划
self.plan_list = []
# 可用箱体数量
self.avail_list = avail_list
# 可用平面列表
self.plane_list = plane_list
# 备用平面列表
self.spare_plane_list = []
# 当前排样重量
self.weight = weight
# 当前排样体积
self.volume = 0
# 选择平面
def select_plane(ps: PackingState):
# 选最低的平面
min_z = min([p.z for p in ps.plane_list])
temp_planes = [p for p in ps.plane_list if p.z == min_z]
if len(temp_planes) == 1:
return temp_planes[0]
# 相同高度的平面有多个的话，选择面积最小的平面
min_area = min([p.lx * p.ly for p in temp_planes])
temp_planes = [p for p in temp_planes if p.lx * p.ly == min_area]
if len(temp_planes) == 1:
return temp_planes[0]
# 较狭窄的
min_narrow = min([p.lx/p.ly if p.lx <= p.ly else p.ly/p.lx for p in temp_planes])
new_temp_planes = []
for p in temp_planes:
narrow = p.lx/p.ly if p.lx <= p.ly else p.ly/p.lx
if narrow == min_narrow:
new_temp_planes.append(p)
if len(new_temp_planes) == 1:
return new_temp_planes[0]
# x坐标较小
min_x = min([p.x for p in new_temp_planes])
new_temp_planes = [p for p in new_temp_planes if p.x == min_x]
if len(new_temp_planes) == 1:
return new_temp_planes[0]
# y坐标较小
min_y = min([p.y for p in new_temp_planes])
new_temp_planes = [p for p in new_temp_planes if p.y == min_y]
return new_temp_planes[0]
# 将某平面从可用平面列表转移到备用平面列表
def disable_plane(ps: PackingState, plane: Plane):
ps.plane_list.remove(plane)
ps.spare_plane_list.append(plane)
# 生成简单块
def gen_simple_block(init_plane: Plane, box_list, num_list, max_height, can_rotate=False):
block_table = []
for box in box_list:
for nx in np.arange(num_list[box.type]) + 1:
for ny in np.arange(num_list[box.type] / nx) + 1:
for nz in np.arange(num_list[box.type] / nx / ny) + 1:
if box.lx * nx <= init_plane.lx and box.ly * ny <= init_plane.ly and box.lz * nz <= max_height - init_plane.z:
# 该简单块需要的立体箱子数量
requires = np.full_like(num_list, 0)
requires[box.type] = int(nx) * int(ny) * int(nz)
# 简单块
block = Block(lx=box.lx * nx, ly=box.ly * ny, lz=box.lz * nz, require_list=requires)
# 简单块填充体积
block.volume = box.lx * nx * box.ly * ny * box.lz * nz
# 简单块重量
block.weight = int(nx) * int(ny) * int(nz) * box.weight
block_table.append(block)
if can_rotate:
# 物品朝向选择90度进行堆叠
if box.ly * nx <= init_plane.lx and box.lx * ny <= init_plane.ly and box.lz * nz <= max_height - init_plane.z:
requires = np.full_like(num_list, 0)
requires[box.type] = int(nx) * int(ny) * int(nz)
# 简单块
block = Block(lx=box.ly * nx, ly=box.lx * ny, lz=box.lz * nz, require_list=requires, box_rotate=True)
# 简单块填充体积
block.volume = box.ly * nx * box.lx * ny * box.lz * nz
# 简单块重量
block.weight = int(nx) * int(ny) * int(nz) * box.weight
block_table.append(block)
return block_table
# 生成可行块列表
def gen_block_list(plane: Plane, avail, block_table, max_height, avail_weight=sys.maxsize):
block_list = []
for block in block_table:
# 块中需要的箱子数量必须小于最初的待装箱的箱子数量
# 块的尺寸必须小于放置空间尺寸
# 块的重量必须小于可放置重量
if (np.array(block.require_list) <= np.array(avail)).all() and block.lx <= plane.lx and block.ly <= plane.ly \
and block.lz <= max_height - plane.z and block.weight <= avail_weight:
block_list.append(block)
return block_list
# 查找下一个可行块
def find_block(plane: Plane, block_list, ps: PackingState):
# 平面的面积
plane_area = plane.lx * plane.ly
# 放入块后，剩余的最小面积
min_residual_area = min([plane_area - b.lx * b.ly for b in block_list])
# 剩余面积相同，保留最大体积的块
candidate = [b for b in block_list if plane_area - b.lx * b.ly == min_residual_area]
# 可用平面最大高度
max_plane_height = min([p.z for p in ps.plane_list])
_candidate = sorted(candidate, key=lambda x: x.volume, reverse=True)
# if max_plane_height == 0:
# # 第一次放置体积最大的块
# _candidate = sorted(candidate, key=lambda x: x.volume, reverse=True)
# else:
# # 选择平面时尽量使放置物品后与已经放置的物品平齐
# _candidate = sorted(candidate, key=lambda x: x.lz + plane.z - max_plane_height)
# _candidate = sorted(candidate, key=lambda x: x.volume + ps.volume - 2440*1220*1000)
return _candidate[0]
# 裁切出新的剩余空间（有稳定性约束）
def gen_new_plane(plane: Plane, block: Block):
# 块顶部的新平面
rs_top = Plane(plane.x, plane.y, plane.z + block.lz, block.lx, block.ly)
# 底部平面裁切
if block.lx == plane.lx and block.ly == plane.ly:
return rs_top, None, None
if block.lx == plane.lx:
return rs_top, Plane(plane.x, plane.y + block.ly, plane.z, plane.lx, plane.ly - block.ly), None
if block.ly == plane.ly:
return rs_top, Plane(plane.x + block.lx, plane.y, plane.z, plane.lx - block.lx, block.ly), None
# 比较两种方式中面积较大的两个子平面，选择有最大面积子平面的生成方式
rsa1 = Plane(plane.x, plane.y + block.ly, plane.z, plane.lx, plane.ly - block.ly)
rsa2 = Plane(plane.x + block.lx, plane.y, plane.z, plane.lx - block.lx, block.ly)
rsa_bigger = rsa1 if rsa1.lx * rsa1.ly >= rsa2.lx * rsa2.ly else rsa2
rsb1 = Plane(plane.x, plane.y + block.ly, plane.z, block.lx, plane.ly - block.ly)
rsb2 = Plane(plane.x + block.lx, plane.y, plane.z, plane.lx - block.lx, plane.ly)
rsb_bigger = rsb1 if rsb1.lx * rsb1.ly >= rsb2.lx * rsb2.ly else rsb2
if rsa_bigger.lx * rsa_bigger.ly >= rsb_bigger.lx * rsb_bigger.ly:
return rs_top, rsa1, rsa2
else:
return rs_top, rsb1, rsb2
# 计算平面浪费面积
def plane_waste(ps: PackingState, plane: Plane, block_table, max_height, max_weight=sys.maxsize):
# 浪费面积
waste = 0
if plane:
block_list = gen_block_list(plane, ps.avail_list, block_table, max_height, max_weight - ps.weight)
if len(block_list) > 0:
block = find_block(plane, block_list, ps)
waste = plane.lx * plane.ly - block.lx * block.ly
else:
waste = plane.lx * plane.ly
return waste
# 判断平面是否可以放置物品
def can_place(ps: PackingState, plane: Plane, block_table, max_height, max_weight=sys.maxsize):
if plane is None:
return False
block_list = gen_block_list(plane, ps.avail_list, block_table, max_height, max_weight - ps.weight)
return True if len(block_list) > 0 else False
# 用块填充平面
def fill_block(ps: PackingState, plane: Plane, block: Block):
# 更新可用箱体数目
ps.avail_list = (np.array(ps.avail_list) - np.array(block.require_list)).tolist()
# 更新放置计划
place = Place(plane, block)
ps.plan_list.append(place)
# 更新体积利用率
ps.volume = ps.volume + block.volume
# 产生三个新的平面
rs_top, rs1, rs2 = gen_new_plane(plane, block)
# 移除裁切前的平面
ps.plane_list.remove(plane)
# 装入新的可用平面
if rs_top:
ps.plane_list.append(rs_top)
if rs1:
ps.plane_list.append(rs1)
if rs2:
ps.plane_list.append(rs2)
# 合并平面
def merge_plane(ps: PackingState, plane: Plane, block_table, max_height, max_weight=sys.maxsize):
# print("合并平面开始了")
for ns in ps.plane_list + ps.spare_plane_list:
# 不和自己合并
if plane == ns:
continue
# 找相邻平面
is_adjacent, ms1, ms2 = plane.adjacent_with(ns)
if is_adjacent:
# print("有相邻平面呦")
block_list = gen_block_list(ns, ps.avail_list, block_table, max_height, max_weight - ps.weight)
# 相邻平面本身能放入至少一个剩余物品
if len(block_list) > 0:
block = find_block(ns, block_list, ps)
# 计算相邻平面和原平面浪费面积的总和
ws1 = ns.lx * ns.ly - block.lx * block.ly + plane.lx * plane.ly
# 计算合并后平面的总浪费面积
ws2 = plane_waste(ps, ms1, block_table, max_height, max_weight) + plane_waste(ps, ms2, block_table, max_height, max_weight)
# 合并后，浪费更小，则保留合并
if ws1 > ws2:
# 保留平面合并
ps.plane_list.remove(plane)
if ns in ps.plane_list:
ps.plane_list.remove(ns)
else:
ps.spare_plane_list.remove(ns)
if ms1:
ps.plane_list.append(ms1)
if ms2:
ps.plane_list.append(ms2)
return
else:
# 放弃平面合并，寻找其他相邻平面
continue
# 相邻平面本身无法放入剩余物品
else:
# 合共后产生一个平面
if ms2 is None:
# 能放物品，则保留平面合并
if can_place(ps, ms1, block_table, max_height, max_weight):
ps.plane_list.remove(plane)
if ns in ps.plane_list:
ps.plane_list.remove(ns)
else:
ps.spare_plane_list.remove(ns)
ps.plane_list.append(ms1)
return
elif ms1.lx * ms1.ly > plane.lx * plane.ly and ms1.lx * ms1.ly > ns.lx * ns.ly:
ps.plane_list.remove(plane)
if ns in ps.plane_list:
ps.plane_list.remove(ns)
else:
ps.spare_plane_list.remove(ns)
# ps.spare_plane_list.append(ms1)
ps.plane_list.append(ms1)
return
else:
continue
# 合并后产生两个平面
else:
if (not can_place(ps, ms1, block_table, max_height, max_weight)) and (not can_place(ps, ms2, block_table, max_height, max_weight)):
if (ms1.lx * ms1.ly > plane.lx * plane.ly and ms1.lx * ms1.ly > ns.lx * ns.ly) or (ms2.lx * ms2.ly > plane.lx * plane.ly and ms2.lx * ms2.ly > ns.lx * ns.ly):
ps.plane_list.remove(plane)
if ns in ps.plane_list:
ps.plane_list.remove(ns)
else:
ps.spare_plane_list.remove(ns)
ps.spare_plane_list.append(ms1)
ps.spare_plane_list.append(ms2)
return
else:
continue
else:
ps.plane_list.remove(plane)
if ns in ps.plane_list:
ps.plane_list.remove(ns)
else:
ps.spare_plane_list.remove(ns)
if can_place(ps, ms1, block_table, max_height, max_weight):
ps.plane_list.append(ms1)
else:
ps.spare_plane_list.append(ms1)
if can_place(ps, ms2, block_table, max_height, max_weight):
ps.plane_list.append(ms2)
else:
ps.spare_plane_list.append(ms2)
return
# 若对平面列表和备用平面列表搜索完毕后，最终仍没有找到可合并的平面，则将目标平面从平面列表移入备用平面列表
disable_plane(ps, plane)
# 构建箱体坐标，用于绘图
def build_box_position(block, init_pos, box_list):
# 箱体类型索引
box_idx = (np.array(block.require_list) > 0).tolist().index(True)
if box_idx > -1:
# 所需箱体
box = box_list[box_idx]
# 箱体的相对坐标
if block.box_rotate:
nx = block.lx / box.ly
ny = block.ly / box.lx
x_list = (np.arange(0, nx) * box.ly).tolist()
y_list = (np.arange(0, ny) * box.lx).tolist()
else:
nx = block.lx / box.lx
ny = block.ly / box.ly
x_list = (np.arange(0, nx) * box.lx).tolist()
y_list = (np.arange(0, ny) * box.ly).tolist()
nz = block.lz / box.lz
z_list = (np.arange(0, nz) * box.lz).tolist()
# 箱体的绝对坐标
dimensions = (np.array([x for x in product(x_list, y_list, z_list)]) + np.array([init_pos[0], init_pos[1], init_pos[2]])).tolist()
# 箱体的坐标及尺寸
if block.box_rotate:
return sorted([d + [box.ly, box.lx, box.lz] for d in dimensions], key=lambda x: (x[0], x[1], x[2])), box_idx
else:
return sorted([d + [box.lx, box.ly, box.lz] for d in dimensions], key=lambda x: (x[0], x[1], x[2])), box_idx
return None, None
# 绘制排样结果
def draw_packing_result(problem: Problem, ps: PackingState):
# 绘制结果
fig = plt.figure()
ax1 = fig.gca(projection='3d')
# 绘制容器
plot_linear_cube(ax1, 0, 0, 0, problem.container.lx, problem.container.ly, problem.height_limit)
for p in ps.plan_list:
# 绘制箱子
box_pos, _ = build_box_position(p.block, (p.plane.x, p.plane.y, p.plane.z), problem.box_list)
positions = []
sizes = []
colors = ["yellow"] * len(box_pos)
for bp in sorted(box_pos, key=lambda x: (x[0], x[1], x[2])):
positions.append((bp[0], bp[1], bp[2]))
sizes.append((bp[3], bp[4], bp[5]))
pc = plotCubeAt(positions, sizes, colors=colors, edgecolor="k")
ax1.add_collection3d(pc)
plt.title('Cube{}'.format(0))
plt.show()
# plt.savefig('3d_lowest_plane_packing.png', dpi=800)
# 基本启发式算法
def basic_heuristic(problem: Problem):
# 生成简单块
block_table = gen_simple_block(problem.container, problem.box_list, problem.num_list, problem.height_limit, problem.rotate)
# 初始化排样状态
ps = PackingState(avail_list=problem.num_list)
# 开始时，剩余空间堆栈中只有容器本身
ps.plane_list.append(Plane(problem.container.x, problem.container.y, problem.container.z, problem.container.lx,problem.container.ly))
max_used_high = 0
# 循环直到所有平面使用完毕
while ps.plane_list:
# 选择平面
plane = select_plane(ps)
# 查找可用块
block_list = gen_block_list(plane, ps.avail_list, block_table, problem.height_limit, problem.weight_limit - ps.weight)
if block_list:
# 查找下一个近似最优块
block = find_block(plane, block_list, ps)
# 填充平面
fill_block(ps, plane, block)
# 更新排样重量
ps.weight += block.weight
# 更新最大使用高度
if plane.z + block.lz > max_used_high:
max_used_high = plane.z + block.lz
else:
# 合并相邻平面
merge_plane(ps, plane, block_table, problem.height_limit, problem.weight_limit)
# 板材的位置信息
box_pos_info = [[] for _ in problem.num_list]
for p in ps.plan_list:
box_pos, box_idx = build_box_position(p.block, (p.plane.x, p.plane.y, p.plane.z), problem.box_list)
for bp in box_pos:
box_pos_info[box_idx].append((bp[0], bp[1], bp[2]))
# 计算容器利用率
used_volume = problem.container.lx * problem.container.ly * max_used_high
used_ratio = round(float(ps.volume) * 100 / float(used_volume), 3) if used_volume > 0 else 0
# # 绘制排样结果图
draw_packing_result(problem, ps)
return ps.avail_list, used_ratio, max_used_high, box_pos_info, ps
# 主算法
def simple_test():
# 容器底面
container = Plane(0, 0, 0, 2440, 1220)
# 箱体列表
box_list = [Box(lx=2390, ly=70, lz=10, weight=3001, type=0),
Box(lx=2390, ly=50, lz=10, weight=10, type=1),
Box(lx=625, ly=210, lz=10, weight=5, type=2),
Box(lx=625, ly=110, lz=10, weight=5, type=3),
Box(lx=2160, ly=860, lz=10, weight=5, type=4),
Box(lx=860, ly=140, lz=10, weight=5, type=5),
Box(lx=860, ly=120, lz=10, weight=5, type=6)]
num_list = [200, 3, 200, 180, 20, 5, 10]
# 问题
problem = Problem(container=container, height_limit=300, weight_limit=4000, box_list=box_list, num_list=copy.copy(num_list))
# 具体计算
new_avail_list, used_ratio, used_high, box_pos_, _ = basic_heuristic(problem)
# 箱体原始数量
print(num_list)
# 剩余箱体
print(new_avail_list)
# 利用率
print(used_ratio)
if __name__ == "__main__":
simple_test()算法运行结果如下：
本文理论部分参考上海交通大学硕士论文《三维装箱问题的混合遗传算法研究》，论文作者和导师都很牛，读者可以自行百度获取论文原文
标签：ps,list,self,水平面,plane,启发式,装箱,lx,ly From： https://www.cnblogs.com/guangzhiruijie/p/17349742.html