pulp(线性规划模块)

模块下载

pip install pulp

常用函数

LpProblem(name=‘NoName’, sense=1)

参数

• name
• sense:LpMinimize(default)或者LpMaximize

重要的属性

• object.objective返回LpAffineExpression对象（即线性规划问题的目标函数，eg,1*x_0+ -3*x_1+3）
• object.constraints返回LpConstraints对象（即线性规划问题的约束条件，字典类型）
• object.status返回LpStatus对象（即线性规划问题的状态）

LpStatus key	string value	numerical value
constants.LpStatusOptimal	Optimal	1
constants.LpStatusNotSolved	Not Solved	0
constants.LpStatusInfeasible	Infeasible	-1
constants.LpStatusUnbounded	Unbounded	-2
constants.LpStatusUndefined	Undefined	-3

重要的方法

• object.solve(solver=None, **kwargs)

LpVariable(name, lowBound=None, upBound=None, cat=‘Continuous’, e=None)

参数

• name 变量名称
• lowbound 变量下限
• upBound 变量上限
• cat 变量类型，Integer、Binary或Continuous(default)

LpAffineExpression(e=None, constant=0, name=None)

• e
  • None 空白表达式
  • dict 键为变量名，值为参数
  • list、generator of 2-tuples dict.items()
  • LpElement

lpSum(vector)

• vector list求和

LpConstraint(e=None, sense=0, name=None, rhs=None)

• e LpAffineExpression对象
• sense LpConstraintEQ、LpConstraintGE、LpConstraintLE对象
• name 名称
• rhs 约束目标，数值型

应用

• 目标函数
  $z=160x_{11}+130x_{12}+220x_{13}+170x_{14}+140x_{21}+130x_{22}+190x_{23}+150x_{24}+190x_{31}+200x_{32}+230x_{33}$
• 约束条件
  $x_{11}+x_{12}+x_{13}+x_{14}=50$
  $x_{21}+x_{22}+x_{23}+x_{24}=60$
  $x_{31}+x_{32}+x_{33}=50$
  $30\le x_{11}+x_{21}+x_{31}\le 80$
  $70\le x_{12}+x_{22}+x_{32}\le 140$
  $10\le x_{13}+x_{23}+x_{33}\le 30$
  $10\le x_{14}+x_{24}\le 50$

from pulp import *

problem = LpProblem('myPro', LpMinimize)
# 定义变量
x11 = LpVariable("x11", lowBound=0)
x12 = LpVariable("x12", lowBound=0)
x13 = LpVariable("x13", lowBound=0)
x14 = LpVariable("x14", lowBound=0)
x21 = LpVariable("x21", lowBound=0)
x22 = LpVariable("x22", lowBound=0)
x23 = LpVariable("x23", lowBound=0)
x24 = LpVariable("x23", lowBound=0)
x31 = LpVariable("x31", lowBound=0)
x32 = LpVariable("x32", lowBound=0)
x33 = LpVariable("x33", lowBound=0)

X = [x11, x12, x13, x14, x21, x22, x23, x24, x31, x32, x33]
c = [160, 130, 220, 170, 140, 130, 190, 150, 190, 200, 230]

# 目标函数
z = 0
for i in range(len(X)):
	z += X[i]*c[i]
prob += z

# 载入约束变量
prob += x11+x12+x13+x14 == con[0]# 约束条件1
prob += x21+x22+x23+x24 == con[1]
prob += x31+x32+x33 == con[2]

prob += x11+x21+x31 <= con[3]
prob += x11+x21+x31 >= con[4]

prob += x12 + x22 + x32 <= con[5]
prob += x12 + x22 + x32 >= con[6]

prob += x13 + x23 + x33 <= con[7]
prob += x13 + x23 + x33 >= con[8]

prob += x14 + x24 <= con[9]
prob += x14 + x24 >= con[10]

# 求解
status = prob.solve()

# 展示结果
for i in prob.variables():
	print(i.varValue)