[英]ILP: Exclusive range for variable
In an ILP, How can I write a constraint "X is not in the interval [Y, Y+10]"?在 ILP 中,如何编写约束“X不在[Y,Y+10] 区间内”?
Is it even possible?有可能吗?
You didn't say, but I'm assuming x
and y
are non-negative integers and that the range you indicate to avoid is inclusive of endpoints...您没有说,但我假设
x
和y
是非负整数,并且您指示要避免的范围包括端点...
You have an "or" condition there, so you will need to introduce a helper or "indicator" variable to handle the or condition , call it z
, and a (constant) parameter for a reasonable upper bound on y
, call it M
:你在那里有一个“或”条件,所以你需要引入一个帮助器或“指示器”变量来处理或条件,称之为
z
,以及一个(常量)参数用于y
的合理上限,称之为M
:
z ∈ {0, 1} # 0 if below y, 1 if above y+10
M > reasonable_upper_bound(y)
Then 2 constraints based on that info to either constrain x to the lower set of values or the upper, excluding the interval (of disinterest):然后基于该信息的 2 个约束将x 约束到较低的一组值或较高的值,不包括间隔(不感兴趣):
x <= (y - 1) + z * M
x >= (y + 10 + 1) * z
Truth Table:真值表:
z=0 z=1
x <= y-1 ~M
x >= 0 y + 11
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