Re: [Help-glpk] Modeling forced constraints with binary variables

[glpk xypron]

Hello Nilo,

GLPK is a solver for linear problems, hence products of variables
are not allowed.

>          A[k] >= A[i] * A[j];
If A is an array of binaries you could use a sum:
A[k] + 1 >= A[k-1] + A[k+1];

Best regards

Xypron




-------- Original-Nachricht --------
> Datum: Mon, 31 Oct 2011 18:38:49 -0200
> Von: Nilo Cesar Teixeira <address@hidden>
> An: address@hidden
> Betreff: [Help-glpk] Modeling forced constraints with binary variables

> Hi all,
> 
> Can you please advise on the following problem ?
> 
> Suppose I have an 1-dimensional array of binary variables, in which
> patterns like these are ok:
> 
> A = 1110000;
> A = 0000011;
> A = 0000000;
> A = 1111111;
> 
> But this pattern is NOT allowed:
> 
> A = 1110111;
> 
> So, a zero should not occur if it is surrounded by ones.
> 
> I tried to model this, and until now I'm using forced constraints based on
> this pseudo-algorithm (assuming A indexing is one-based for simplicity):
> 
> for i := 1 to count(A) do
>    for j := i+2 to count(A) do
>       for k := i+1 to j-1 do
>          A[k] >= A[i] * A[j];
>       next
>    next
> next
> 
> So, if A[k] is zero, then A[i] and A[j] can't be one!
> 
> This is working in other commercial solver, but I would like to make this
> work on glpk.
> 
> Nevertheless, as I compile it fails saying that the constraint is not
> linear.
> 
> Even the commercial solver states the compiling model as INLP
> (non-linear),
> but it solves it in seconds.
> 
> Is there any way this could work on glpk ?
> 
> Thank you.
> 
> -- 
> *Nilo Cesar Teixeira*
> address@hidden
> (55) (11) 8571-5314

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