[英]Get minimum of maximize value on pulp objective function
I'm trying to use pulp to get minimum value U(X)
of following objective function,我正在尝试使用纸浆来获得以下目标函数的最小值U(X)
,
where x_{f,i,v}
is binary value.其中x_{f,i,v}
是二进制值。
And I'm having problem while writing max()
when set an objective function to pulp.LpProblem
.在将目标函数设置为pulp.LpProblem
时,我在编写max()
时遇到了问题。
What I do is use python inner function max()
but it gives me an error.我所做的是使用 python 内部函数max()
但它给了我一个错误。 Seems like it cannot be used to pulp.好像不能用来打浆。
for each_sfc in self.SFCs:
vnf_id_list = list()
for each_VNF in each_sfc.VNF_list:
vnf_id_list.append(str(each_VNF.ID))
new_sfc_vars = LpVariable.dicts(
name='X',
indexs=vnf_id_list,
lowBound=0,
upBound=1,
cat='Continuous'
)
for each_key in new_sfc_vars.keys():
new_sfc_vars[each_key] = 1 - new_sfc_vars[each_key]
self.sfc_vars.append(new_sfc_vars)
self.LP_model = LpProblem(
name="Static backup",
sense=LpMinimize
)
for each_SFC, each_vars in zip(self.SFCs, self.sfc_vars):
self.LP_model.objective += each_SFC.backup_cost * max(each_vars.values())
print(self.LP_model.objective)
How can I use max()
with pulp or how can I reformulate the code?如何将max()
与纸浆一起使用或如何重新编写代码?
This is a very basic question.这是一个非常基本的问题。
max()
is not linear. max()
不是线性的。 Linear expressions look like a1*x1+a2*x2+...
.线性表达式看起来像a1*x1+a2*x2+...
。 PuLP is for linear models only, so it only allows linear expressions in the objective and the constraints. PuLP 仅用于线性模型,因此它只允许目标和约束中的线性表达式。 Note that some modeling tools have a max function, but they typically linearize this under the hood.请注意,某些建模工具具有 max 函数,但它们通常会在幕后对其进行线性化。
A very standard formulation for a construct like min sum(i, max(j, x(i,j))
is像min sum(i, max(j, x(i,j))
这样的构造的一个非常标准的公式是
min sum(i, y(i)) y(i) >= x(i,j) for all i,j
Just consult any LP textbook.只需查阅任何 LP 教科书即可。 It will explain this formulation.它将解释这个公式。 Often this is called minimax
.通常这称为minimax
。
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