纸浆添加约束，即至少一个LpAffineExpression等于1 [英] Pulp add constraint that at least one LpAffineExpression is equal to one

问题描述

说我有一个这样定义的PuLP模型: model = pulp.LpProblem('',pulp.LpMaximize)

Say I have a PuLP model defined as thus: model = pulp.LpProblem('',pulp.LpMaximize)

我添加了一个目标函数(没关系)

And I have added an objective function (it does not matter)

现在我有一个LpAffineExpression对象的列表: lps = [l1, l2, l3, ...]

Now I have a list of LpAffineExpression objects: lps = [l1, l2, l3, ...]

我想将这些LpAffineExpression之一评估为1的约束添加到模型中.我将如何做?

I want to add to the model the constraint that one of these LpAffineExpression evaluates to 1. How would I do so?

基本上，我要寻找的是语法正确的方式来执行以下操作:

Essentially what I'm looking for is the syntactically correct way to do the following:

model += (l1 == 1 OR l2 == 1 OR l3 == 1 OR ...)

请注意，我不知道lps列表中有多少个LpAffineExpression对象，因此无法对其进行硬编码.

Note that I do not know how many how many LpAffineExpression objects are in the lps list, so I cannot hardcode it in.

换句话说，我正在寻找一种在模型中对一组LpAffineExpression进行分组的方法，这样就只需要实现一个即可.

In other words, I am looking for a way to group a set of LpAffineExpression in the model, such that only one has to be fulfilled.

推荐答案

在线性或整数编程中没有或".但是，您可以使用二进制变量来模拟这种OR构造. (或者，如果不希望使用big-M，则使用SOS1变量；我不确定Pulp支持SOS1变量的扩展范围.)

There is no "OR" in linear or integer programming. However, you can use binary variables to simulate such an OR construct. (Or SOS1 variables if big-M's are undesirable; I am not sure to what extend Pulp supports SOS1 variables).

这个想法是:

1 - M * (1-δ(i)) <= L(i) <= 1 + M * (1-δ(i)) 
sum(i, δ(i)) >= 1 
δ(i) ∈ {0,1}

• 显然L(i)是您的l1,l2,l3,...
• δ(i)是一个二进制变量，指示是否L(i)=1.我们有δ(i)=1 ⇒ L(i)=1.
• 常量M可以设置为L(i)的上下限.
• Obviously the L(i) are your l1,l2,l3,...
• δ(i) is a binary variable indicating if L(i)=1. We have δ(i)=1 ⇒ L(i)=1.
• The constants M can be set to lower and upper bounds of L(i).

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