28、二维装箱
作者：互联网
from pyscipopt import Model, quicksum
from vtk import *
import vtk
import random as rd
import time
import numpy as np
import functools
#二维商品排序用
def cmp_2d(x,y):
if x[0] < y[0]:
return -1
elif x[0] > y[0]:
return 1
elif x[1] < y[1]:
return -1
elif x[1] > y[1]:
return 1
else:
return 0
#数据生成，输入为箱子种类数，箱子最大长、最小长、最大宽、最小宽、商品个数、商品最大长、最小长、最大宽、最小宽
#输出为生成的箱子列表和商品列表
def data_generate_2d(nums_box, max_edge_box, min_edge_box, nums_good, max_edge_good, min_edge_good):
#随机生成箱子
boxs = []
for i in range(nums_box):
boxs.append([int((max_edge_box-min_edge_box) * rd.random() + min_edge_box), int((max_edge_box-min_edge_box) * rd.random() + min_edge_box)])
#随机生成商品
goods = []
for i in range(nums_good):
goods.append([int((max_edge_good-min_edge_good) * rd.random() + min_edge_good), int((max_edge_good-min_edge_good) * rd.random() + min_edge_good)])
return boxs,goods
def data_pre(boxs, goods):
#箱子长边作长，放前面
for box in boxs:
if box[0] < box[1]:
box[0],box[1] = box[1],box[0]
#箱子排序，大的放前面
boxs = sorted(boxs, key=functools.cmp_to_key(cmp_2d), reverse=True)
#箱子种类去重
i = 0
while i < len(boxs) - 1:
j = i + 1
while j < len(boxs):
if boxs[i][0] == boxs[j][0] and boxs[i][1] == boxs[j][1]:
del boxs[j]
else:
j += 1
i += 1
#商品长边作长，放前面
for good in goods:
if good[0] < good[1]:
good[0],good[1] = good[1],good[0]
#商品排序，大的放前面
goods = sorted(goods, key=functools.cmp_to_key(cmp_2d), reverse=True)
return boxs,goods
#检验是否每个商品都能有一个箱子放下它
def check_2d(boxs, goods):
for good in goods:
can_put = False
for box in boxs:
if good[0] <= box[0] and good[1] <= box[1]:
can_put = True
break
if not can_put:
print(good,"太大，无合适箱子")
return False
return True
#二维装箱整数规划
def IP_2d(boxs, goods, time_limit):
m = len(boxs)
n = len(goods)
M = max([max(boxs[i]) for i in range(m)])*10
model = Model("IP_2d")
#对X、Y，i为包裹下标，j为商品下标，x[i][j]=1代表第j件商品放进第i个包裹里，y[i]=1表示开启第i个包裹
X = [[model.addVar(vtype="B", name="X[%s,%s]" % (i, j)) for j in range(n)] for i in range(m*n)]
Y = [model.addVar(vtype="B", name="Y[%s]" % i) for i in range(m*n)]
#包裹面积向量，[n个boxs[0],n个boxs[1],...,n个boxs[m-1]]
c = [boxs[i][0]*boxs[i][1] for i in range(len(boxs)) for j in range(len(goods))]
cb = [boxs[i] for i in range(len(boxs)) for j in range(len(goods))]
#码放形式，1代表(l,w), 0代表(w,l)
type_place = [model.addVar(vtype="B", name="tp[%s]" % i) for i in range(n)]
#码放长、宽、坐标x、y、z
L = [model.addVar(vtype="I", name="L[%s]" % i) for i in range(n)]
W = [model.addVar(vtype="I", name="W[%s]" % i) for i in range(n)]
x = [model.addVar(vtype="I", name="x[%s]" % i) for i in range(n)]
y = [model.addVar(vtype="I", name="y[%s]" % i) for i in range(n)]
#选择变量，fx[i][j]=1代表i在j的左边（小），fy[i][j]=1同理，f[i][j][k]=1代表j、k同时在第i个箱子中
fx = [[model.addVar(vtype="B", name="fx[%s,%s]" % (i, j)) for j in range(n)] for i in range(n)]
fy = [[model.addVar(vtype="B", name="fy[%s,%s]" % (i, j)) for j in range(n)] for i in range(n)]
f = [[[model.addVar(vtype="B", name="f[%s,%s,%s]" % (i, j, k)) for k in range(n)] for j in range(n)] for i in range(m*n)]
#以总包裹体积最小（即填充率最大）为目标
model.setObjective(quicksum(Y[i]*c[i] for i in range(m*n)), "minimize")
# 使用前必须开启
for i in range(m * n):
for j in range(n):
model.addCons(X[i][j] - Y[i] <= 0)
#每个商品都能被装下
for j in range(n):
model.addCons(quicksum(X[i][j] for i in range(m * n)) == 1)
#码放长宽约束
for j in range(n):
model.addCons(L[j] - goods[j][0] * type_place[j] - goods[j][1] * (1 - type_place[j]) == 0)
model.addCons(W[j] - goods[j][1] * type_place[j] - goods[j][0] * (1 - type_place[j]) == 0)
#位置约束，大于0，不超过边界，不相交
for j in range(n):
model.addCons(x[j] >= 0)
model.addCons(y[j] >= 0)
for i in range(m*n):
for j in range(n):
model.addCons(x[j] + L[j] - cb[i][0] - M*(1 - X[i][j]) <= 0)
model.addCons(y[j] + W[j] - cb[i][1] - M*(1 - X[i][j]) <= 0)
for j in range(n):
for k in range(j+1,n):
model.addCons(x[j] + L[j] - x[k] - M*(1 - fx[j][k]) <= 0)
model.addCons(x[k] + L[k] - x[j] - M*(1 - fx[k][j]) <= 0)
model.addCons(y[j] + W[j] - y[k] - M*(1 - fy[j][k]) <= 0)
model.addCons(y[k] + W[k] - y[j] - M*(1 - fy[k][j]) <= 0)
for i in range(m*n):
for j in range(n):
for k in range(j+1,n):
model.addCons(X[i][j] + X[i][k] - 1 - M*(1 - f[i][j][k]) <= 0)
for j in range(n):
for k in range(j+1,n):
model.addCons(fx[j][k] + fx[k][j] + fy[j][k] + fy[k][j] + quicksum(f[i][j][k] for i in range(m*n)) >= m*n)
#设置求解时间
model.setRealParam("limits/time", time_limit)
model.optimize()
print("\ngap:",model.getGap())
#拿结果
X1 = [[round(model.getVal(X[i][j])) for j in range(n)] for i in range(m * n)]
L1 = [round(model.getVal(L[i])) for i in range(n)]
W1 = [round(model.getVal(W[i])) for i in range(n)]
x1 = [round(model.getVal(x[i])) for i in range(n)]
y1 = [round(model.getVal(y[i])) for i in range(n)]
L_box = []
L_goods = []
L_coordinates = []
for i in range(m*n):
goods_i = []
coordinates_i = []
for j in range(n):
if X1[i][j] == 1:
goods_i.append(goods[j])
coordinates_i.append([L1[j],W1[j],x1[j],y1[j]])
if len(goods_i) > 0:
L_box.append(cb[i])
L_goods.append(goods_i)
L_coordinates.append(coordinates_i)
return L_box, L_goods, L_coordinates, model.getGap()
#任务分流汇总
#给一系列箱子和商品（箱子可用个数不限），推荐结果
def stacking_2d(boxs, goods, time_limit):
#长宽预处理，降序排序，箱子去重
boxs,goods = data_pre(boxs,goods)
#这里是否所有的商品均至少有一个箱子可以装下，若有商品超出规格则直接返回
if not check_2d(boxs, goods):
return [[], []]
# 多类箱子，应用整数规划求解
L_box, L_goods, L_coordinates, gap = IP_2d(boxs, goods, time_limit)
# # gap较大时，用启发式方法比较，取优
# if gap >= 0.01 and goods_check(goods, L_goods):
# print("尝试采用启发式方法")
# L_box1, L_goods1 = BFD(boxs, goods)
# if sum(L_box) > sum(L_box1) and goods_check(goods, L_goods1):
# print("采用启发式方法")
# L_box, L_goods = L_box1, L_goods1
#
# #结果检验，当求解器的结果有问题（商品数不符时）采用混合BFD求解方案
# if not goods_check(goods, L_goods):
# # BFD
# L_box, L_goods = BFD(boxs, goods)
return L_box, L_goods, L_coordinates
#添加商品图形
def Addcube_2d(ren, coordinate, edge_max, h, x_re, y_re, z_re):
cube = vtk.vtkCubeSource()
cube.SetXLength(coordinate[0]/edge_max)
cube.SetYLength(coordinate[1]/edge_max)
cube.SetZLength(h)
cube.Update()
translation = vtkTransform()
translation.Translate((coordinate[2] + coordinate[0]/2.0)/edge_max + x_re, (coordinate[3] + coordinate[1]/2.0)/edge_max + y_re, h/2.0 + z_re)
transformFilter = vtkTransformPolyDataFilter()
transformFilter.SetInputConnection(cube.GetOutputPort())
transformFilter.SetTransform(translation)
transformFilter.Update()
transformedMapper = vtkPolyDataMapper()
transformedMapper.SetInputConnection(transformFilter.GetOutputPort())
transformedActor = vtkActor()
transformedActor.SetMapper(transformedMapper)
transformedActor.GetProperty().SetColor((rd.uniform(0, 1), rd.uniform(0, 1), rd.uniform(0, 1)))
ren.AddActor(transformedActor)
#一维展示，输入为箱子集和商品集，包裹的箱子和商品集一一对应
def show_2d(L_box, L_coordinates):
nums = len(L_box)
edge_max = max([max(L_box[i]) for i in range(len(L_box))])
#预设参数
CH = 0.5
gap = 0.25
CL_p = 1.1
CW_p = nums + gap * (nums - 1)
CH_p = 0.01
gap = 0.25
x_re = -0.5
y_re = -0.5
z_re = -0.5
#渲染及渲染窗口，并根据捕捉的鼠标事件执行相应的操作
ren = vtk.vtkRenderer()
renWin = vtk.vtkRenderWindow()
renWin.AddRenderer(ren)
iren = vtk.vtkRenderWindowInteractor()
iren.SetRenderWindow(renWin)
"""画容器"""
for i in range(nums):
cube = vtk.vtkCubeSource()
cube.SetXLength(L_box[i][0]/edge_max)
cube.SetYLength(L_box[i][1]/edge_max)
cube.SetZLength(CH)
cube.Update()
translation = vtkTransform()
translation.Translate(L_box[i][0]/edge_max/2.0 + x_re, L_box[i][1]/edge_max/2.0 + i + gap*i + y_re, CH/2.0 + z_re)
transformFilter = vtkTransformPolyDataFilter()
transformFilter.SetInputConnection(cube.GetOutputPort())
transformFilter.SetTransform(translation)
transformFilter.Update()
transformedMapper = vtkPolyDataMapper()
transformedMapper.SetInputConnection(transformFilter.GetOutputPort())
transformedActor = vtkActor()
transformedActor.SetMapper(transformedMapper)
transformedActor.GetProperty().SetColor((1, 1, 1))
transformedActor.GetProperty().SetRepresentationToWireframe()
ren.AddActor(transformedActor)
"""画托盘"""
cube = vtk.vtkCubeSource()
cube.SetXLength(CL_p)
cube.SetYLength(CW_p)
cube.SetZLength(CH_p)
cube.Update()
translation = vtkTransform()
translation.Translate(CL_p/2.0 + x_re, CW_p/2.0 + y_re, -CH_p/2.0 + z_re)
transformFilter = vtkTransformPolyDataFilter()
transformFilter.SetInputConnection(cube.GetOutputPort())
transformFilter.SetTransform(translation)
transformFilter.Update()
transformedMapper = vtkPolyDataMapper()
transformedMapper.SetInputConnection(transformFilter.GetOutputPort())
transformedActor = vtkActor()
transformedActor.SetMapper(transformedMapper)
transformedActor.GetProperty().SetColor((0.2, 0.4, 0.8))
ren.AddActor(transformedActor)
for i in range(len(L_coordinates)):
for j in range(len(L_coordinates[i])):
Addcube_2d(ren, L_coordinates[i][j], edge_max, CH, x_re, i + gap*i + y_re, z_re)
camera = vtk.vtkCamera()
camera.SetPosition(5, -0.5, 2)
camera.SetViewUp(0, 0, 1)
ren.SetActiveCamera(camera)
iren.Initialize()
renWin.Render()
iren.Start()
if __name__ == "__main__":
#生成箱子集和商品集，计算并展示
boxs,goods = data_generate_2d(nums_box = 2, max_edge_box = 20, min_edge_box = 10, nums_good = 10, max_edge_good = 10, min_edge_good = 1)
print(boxs)
print(goods)
L_box, L_goods, L_coordinates= stacking_2d(boxs, goods, time_limit = 100)
print(L_box)
print(L_coordinates)
show_2d(L_box, L_coordinates)
标签：box,goods,max,28,good,二维,edge,装箱,boxs 来源： https://blog.csdn.net/chaoyuzhang/article/details/91049332