如果条件在放大器中 [英] if condition in ampl

问题描述

我是ampl的新手，我想在if条件中使用以下信息:

I am new in ampl and I want to use if condition in ampl with the following information:

我有一个二进制变量X [p，r]，其中{p中的p，R中的r}. 现在，我想进行一个新的约束，使得在X [p，r] = 0的情况下使用变量R [p，r]. 我不知道如何编写它，或者即使放大器不能处理它，我也尝试了以下约束，但是它们没有用:

I have a binary variable X[p,r], where {p in P, r in R}. Now I want to make a new constraint such that the variable R[p,r] is used where X[p,r]=0. I do not know how I can write it or even if the ampl can handle it or not, I tried the following constraint but they did not work:

s.t. a1{r in R, p in P and X[p,r]=0}: 
s.t. a2{r in R p in P and X[p,r]=0};
s.t. a2{r in R ,p in P, and X[p,r]=0};
s.t. a2{r in R, p in P: and X[p,r]=0};

推荐答案

您不能在约束的全部"部分(在AMPL中，{...}内部的部分)中包含决策变量.取而代之的是，您需要在约束本身中构建表示约束仅在X[p,r] = 0处于活动状态的逻辑.这样做的方式取决于约束的类型:> =，=或< =.我将分别编写每种情况，并以通用的方式而不是针对您的问题进行处理.

You cannot include a decision variable in the "for all" part of the constraint (in AMPL, the part inside the {...}). Instead, you need build into the constraint itself the logic that says the constraint is only active if X[p,r] = 0. The way to do that depends on the type of constraint: >=, =, or <=. I'll write each case separately, and I'll do it in a generic way instead of specific to your problem.

在下面的说明中，我假设约束条件写为

In the explanation below, I assume that the constraint is written as

a[1]y[1] + ... + a[n]y[n] >=/=/<= b, 

其中，a[i]和b是常量，而y[i]是决策变量.我还假设如果x = 0希望约束保持不变，其中x是二进制决策变量，并且我们不关心如果x = 1约束是否成立.

where a[i] and b are constants and y[i] are decision variables. I also assume we want the constraint to hold if x = 0, where x is a binary decision variable, and we don't care whether the constraint holds if x = 1.

让M为等于大数的新参数(常量).

Let M be a new parameter (constant) that equals a large number.

大于或等于约束:

约束为a[1]y[1] + ... + a[n]y[n] >= b.将其重写为

a[1]y[1] + ... + a[n]y[n] >= b - Mx.

然后，如果x = 0成立，则约束成立，如果x = 1成立，则该约束无效，因为右侧非常负.

Then, if x = 0, the constraint holds, and if x = 1, it has no effect since the right-hand side is very negative.

(如果所有a[i]均为非负数，则可以改用

(If all of the a[i] are nonnegative, you can instead use

a[1]y[1] + ... + a[n]y[n] >= bx,

更严格.)

小于或等于约束:

约束为a[1]y[1] + ... + a[n]y[n] <= b.将其重写为

a[1]y[1] + ... + a[n]y[n] <= b + Mx.

然后，如果x = 0，则约束成立，而如果x = 1，则由于RHS很大而无效.

Then, if x = 0, the constraint holds, and if x = 1, it has no effect since the RHS is very large.

平等约束:

约束为a[1]y[1] + ... + a[n]y[n] = b.将其重写为

a[1]y[1] + ... + a[n]y[n] <= b + Mx
a[1]y[1] + ... + a[n]y[n] >= b - Mx.

然后，如果x = 0，则相等约束成立，如果x = 1，则约束无效.

Then, if x = 0, the equality constraint holds, and if x = 1, the constraints have no effect.

注意:如果您的模型相对较大，即解决它花费的时间不可忽略，那么您需要小心使用大型M型公式.特别是，您希望M尽可能小，同时仍要强制执行上述约束的逻辑.

Note: If your model is relatively large, i.e., it takes a non-negligible amount of time to solve, then you need to be careful with big-M-type formulations. In particular, you want M to be as small as possible while still enforcing the logic of the constraints above.

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