Pyomo glpk 求解器没有给我最优值

Question

我希望有人能帮助我。我正在练习优化建模，并且正在使用 pyomo glpk 解决以下 LP 问题：

最大 z = 4x1 + 3x2

服从：

• x1 + x2 <= 40
• 2x1 + x2 <= 60
• x1, x2 >= 0

我的代码如下：

# Defining the model
model = pyo.ConcreteModel()

# Decision variables
model.x1 = pyo.Var(within = pyo.NonNegativeReals)
x1 = model.x1
model.x2 = pyo.Var(within = pyo.NonPositiveReals)
x2 = model.x2

# Objective function
model.Obj = pyo.Objective(expr = 4*x1+3*x2, sense = pyo.maximize)

# Constraints
model.Const1 = pyo.Constraint(expr = x1+x2<=40)
model.Const2 = pyo.Constraint(expr = 2*x1+x2<=60)

# Run the solver
optm = SolverFactory('glpk')
results = optm.solve(model)

# Show the results
print(results)
print('Objective function = ', model.Obj())
print('x1 = ', x1())
print('x2 = ', x2())

我得到的结果是：

Problem: 
- Name: unknown
  Lower bound: 120.0
  Upper bound: 120.0
  Number of objectives: 1
  Number of constraints: 3
  Number of variables: 3
  Number of nonzeros: 5
  Sense: maximize
Solver: 
- Status: ok
  Termination condition: optimal
  Statistics: 
    Branch and bound: 
      Number of bounded subproblems: 0
      Number of created subproblems: 0
  Error rc: 0
  Time: 0.012318611145019531
Solution: 
- number of solutions: 0
  number of solutions displayed: 0

Objective function =  120.0
x1 =  30.0
x2 = 0.0

但是，结果应该是：

Object function = 140.0
x1 = 20.0
x2 = 20.0

由于我只使用线性方程，我相信它既是凸的又是凹的，不确定这种情况下是否存在局部最优？

否则，谁能告诉我我做错了什么？

提前非常感谢您的帮助！

Answer 1

您走在正确的道路上。你有一个不幸的打字错误正在困扰着你。您将

x2

的域声明为非 正，您明确希望

pyo.NonNegativeReals

如果您有奇怪的行为，请始终

pprint

和/或

display

您的模型。错误往往很快就会显现出来。

pprint

显示了构造，

display

类似，但显示了带有值的表达式的求值。

2 个其他小问题...我不会重命名你的变量，只需将它们键入即可。另外，我相信 value(var) 是访问值的首选方式。这是经过一些编辑的工作版本。

import pyomo.environ as pyo

# Defining the model
model = pyo.ConcreteModel()

# Decision variables
model.x1 = pyo.Var(within = pyo.NonNegativeReals)
# x1 = model.x1
model.x2 = pyo.Var(within = pyo.NonNegativeReals)
# x2 = model.x2

# Objective function
model.Obj = pyo.Objective(expr = 4*model.x1+3*model.x2, sense = pyo.maximize)

# Constraints
model.Const1 = pyo.Constraint(expr = model.x1+model.x2<=40)
model.Const2 = pyo.Constraint(expr = 2*model.x1+model.x2<=60)

# Run the solver
optm = pyo.SolverFactory('glpk')
results = optm.solve(model)

model.display()

# Show the results
print(results)
print('Objective function = ', pyo.value(model.Obj))
print('x1 = ', pyo.value(model.x1))
print('x2 = ', pyo.value(model.x2))