Searching for MILP constraint to prevent alternation of integer variable

Question

Here is precisely my case: Let's assume a variable x[t] which is a NonNegativeInteger smaller or equal than 3.

So x[t] can be {0,1,2,3}. It's indexed by a time serie.

I would like to prevent x[t] from alternating. Means I would like to disallow

x[0] = 0
x[1] = 1
x[2] = 0

but also

x[0] = 1
x[1] = 2
x[2] = 1

and

x[0] = 2
x[1] = 3
x[2] = 2

I am looking for a constraint to disallow this. Three time steps must be involved in that constraint.

I've tried a couple of constraints. I am not sure if this is even possible with a simple constraint.

Maybe I have to add a variable to make this work. Do you have any experience with that kind of problem?

Thank you in advance!

kur ag · Accepted Answer · 2018-08-29 13:10:34Z

0

You can ensure increasing or decreasing order with below constraints:

x[t] + M(y-1) <= x[t+1]

x[t] + My >= x[t+1]

y:Binary variable (same y is used at all equations)

M:Big number (bigger than possible the biggest value)

answered Aug 29, 2018 at 13:10

kur ag

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4 Comments

programmar Over a year ago

Sorry, maybe I didn’t explain my problem clearly. I want to prevent it from alternating. I don’t want to ensure increasing. So 0,1,0 should be prevented, but 0,1,1,0 should be possible.

kur ag Over a year ago

I think that if "t" is {0,1,2,3}, using different binary varible (y) for last equation set will be enough.

programmar Over a year ago

Can you tell me how?

kur ag Over a year ago

Actually, if being increasing or decreasing order of the first three variable is enough for you, write the equation set for t = 0 and t=1 and make free x[3]. Because there is not relation between x[2] and x[3]. This allows 0,1, 1,0 or 1, 0, 0, 1.

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