Hi Jay,
This is a trickier issue than it might seem at first glace. First off, the
GMPL/MathProg language uses several syntactic constructs to facilitate
modeling such as indexing and logical expressions. These are different
from the linear expressions used to express MILP constraints and objective
functions. The language definition doesn't allow you to mix them up as you
can in some scripting languages (Matlab comes to mind). It's easy to miss
these distinctions when quickly browsing the GMPL language reference. As
Xypron noted, mixing these would lead to nonlinear and nonconvex problems
that are not trivially translated to LP's or MILP's.
Also note that the "Big M" technique commonly used to implement logical
constraints as an MILP needs to be 'tuned' to work effectively. A proper
value of M is data dependent, so the automatic translation of logical
constraints to an MILP is not a trivial issue.
Second, with regard to your application, it sounds like you may need to
introduce a binary decision variable -- say
var y{B} binary;
that is one if b is in set B, and a parameter -- call it
param p{a in A} := some logical expression regarding a
>From here I'm not sure that I understand your problem, but something like
s.t. constr {a in A : p[a] = 1} : sum{b in B} y[b] >= x[a];
may be what you're looking for. But it's not at all clear to me that this
is what you had in mind.
Hope that helps,
Jeff
On Tue, May 7, 2013 at 7:21 AM, Jay Hutfles <[email protected]> wrote:
> I don't think you meant to address Andrew, but thanks for replying.
>
> I realize if-then constraints aren't naturally supported in linear
> programming (or mixed integer programming). But you can formulate
> constraints that are *logically equivalent *to if-then constraints. See
> the whole part about "changing from the form 'if p then q' to 'not p or q.'
> " The constraint is still true under the same conditions of the logical
> implication, so it constrains the binary variables in the same manner.
> Yes, it may not be the most efficient, but it is a proper way to model
> such a constraint in a linear programming problem.
>
>
> On Tue, May 7, 2013 at 5:54 AM, <[email protected]> wrote:
>
>> Hello Andrew,
>>
>> GLPK is a linear programming solver. A constraint with an IF would not be
>> linear.
>>
>> In linear programming you might introduce binary variables for your
>> purpose.
>>
>> Or use a constraint programming solver.
>>
>> Best regards
>>
>> Heinrich Schuchardt
>>
>> http://www.xypron.de
>>
>> Am 07.05.13 um 07:48 schrieb Jay Hutfles
>>
>> > Oh, I don't think there's anything wrong with them. Well, except for
>> how
>> >
>> > I'm trying to use them.
>> >
>> >
>> >
>> > I see that the examples only use them in computable parameters, though.
>> I
>> >
>> > was trying to use them in constraints, and was getting errors along the
>> >
>> > lines of "forall function does not exist" (sorry, I don't have the exact
>> >
>> > error with me). The constraints were of the form:
>> >
>> >
>> >
>> > for all a in A, if x[a] =1 then there exists a b in B such that
>> >
>> > (something or another based on a)
>> >
>> >
>> >
>> > I was having trouble directly implementing constraints of this form, so
>> I
>> >
>> > changed the "if p then q" form to "not p or q" like this:
>> >
>> >
>> >
>> > subject to C {a in A} :
>> >
>> > (1 - x[a]) + (if exists {b in B} (...something or other based on
>> a..)
>> >
>> > then 1 else 0) >= 1;
>> >
>> >
>> >
>> > I'll have to try again in the morning when I'm more awake. Thanks for
>> the
>> >
>> > guidance, Andrew.
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> > On Mon, May 6, 2013 at 11:36 PM, Andrew Makhorin <[email protected]> wrote:
>> >
>> >
>> >
>> > >
>> >
>> > > > Can you provide a link to an example of each? Any help would be
>> >
>> > > > appreciated.
>> >
>> > > >
>> >
>> > >
>> >
>> > > Please see glpk/examples/color.mod (for 'exists') and
>> >
>> > > glpk/examples/egypt.mod (for 'forall').
>> >
>> > >
>> >
>> > > What is wrong with these operators?
>> >
>> > >
>> >
>> > >
>> >
>> > >
>> >
>> > _______________________________________________
>> >
>> > Help-glpk mailing list
>> >
>> > [email protected]
>> >
>> > https://lists.gnu.org/mailman/listinfo/help-glpk
>>
>
>
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