如何在 pyomo 的优化问题中做出正确的约束

Question

我有一个货车修理的优化问题。

  'Lon':   125,        # London
  'Ber':   175,        # Berlin
  'Maa':   225,        # Maastricht
  'Ams':   250,        # Amsterdam
  'Utr':   225,        # Utrecht
  'Hag':   200         # The Hague
}

Supply = {
  'Arn':   600,        # Arnhem
  'Gou':   650         # Gouda
}

T = {
   ('Lon','Arn'): 1000,
   ('Lon','Gou'): 2.5,
   ('Ber','Arn'): 2.5,
   ('Ber','Gou'): 1000,
   ('Maa','Arn'): 1.6,
   ('Maa','Gou'): 2.0,
   ('Ams','Arn'): 1.4,
   ('Utr','Arn'): 0.8,
   ('Utr','Gou'): 1.0,
   ('Hag','Arn'): 1.4,
   ('Hag','Gou'): 0.8
}

T 是所有允许路由的成本。我定义了模型和 objective 函数。

# Step 0: Create an instance of the model
model = ConcreteModel()
model.dual = Suffix(direction=Suffix.IMPORT)

# Step 1: Define index sets
CUS = list(Demand.keys())
SRC = list(Supply.keys())

# Step 2: Define the decision 
model.x = Var(list(T), domain = NonNegativeReals)

# Step 3: Define Objective
model.Cost = Objective(
    expr = sum([T[i]*model.x[i] for i in model.x]),
    sense = minimize)

但是我遇到了约束问题。如果我这样做如下所示，它会抛出一个错误。

# Step 4: Constraints
model.src = ConstraintList()
for s in SRC:
   model.src.add(sum([model.x[c,s] for c in CUS]) <= Supply[s])
       
model.dmd = ConstraintList()
for c in CUS:
   model.dmd.add(sum([model.x[c,s] for s in SRC]) == Demand[c])

错误是这样的：

也许有人知道如何解决约束问题。使其更加灵活。我明白为什么它是一个错误，因为在 T 中并没有所有可能的组合，但它是正确的，一些路线被限制，我不想在优化中使用它们。

Answer 1

你可以先得到这样的可能：

# Step 4: Constraints
model.src = ConstraintList()
for s in SRC:
    cposs = [t[0] for t in T.keys() if t[1] == s]
    model.src.add(sum([model.x[c,s] for c in cposs]) <= Supply[s])

model.dmd = ConstraintList()
for c in CUS:
    sposs = [t[1] for t in T.keys() if t[0] == c]
    model.dmd.add(sum([model.x[c,s] for s in sposs]) == Demand[c])

如何在 pyomo 的优化问题中做出正确的约束

How to make the right constraints in optimization problem in pyomo

optimization

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