CODEWITHSUNDEEP
scip
mudrole1
mudrole1

Reputation: 11

What is the best way to specify constraints containing multiplication of two variables in SCIP?

I am using SCIP Optimization Suite 3.0.2 to in my c++ code to implement a scheduler and I would like to ask you what is the best way to implement constraint such as:

t_i*p + d*p + t_i <=0

where t_i is a continous variable, p is a binary variable, d is a constant. I found the overview of all supported type of constraints: scip constraints and I somehow implemented my problem as a hierarchy of more linear constraints and conjunctions and disjunctions between them, but I have a suspicious that makes the search for a solution hard. Thus, I am interested if there is some more straightforward way, especially for multiplying of two variables.

Upvotes: 1

Views: 584

Answers (2)

Gregor
Gregor

Reputation: 1375

Considering the constraint that you mentioned, there even is a linear formulation, at least if t_i is bounded to be nonnegative: Since p is supposed to be binary, it breaks down to either

  • p = 0 => t_i <= 0, forcing t_i to 0 because of nonnegativity assumed above
  • p = 1 => 2 * t_i <= -d

You can fold this into a single linear constraint, in which p is basically imposing an upper bound on t_i:

t_i + d / 2 * p <= 0

Using SCIP's callable library, you can directly create this constraint as a varbound constraint.

Upvotes: 2

Ambros Gleixner
Ambros Gleixner

Reputation: 21

You can formulate this as a quadratic constraint. See the "Callable library" example,

http://scip.zib.de/doc/examples/CallableLibrary/

in particalur the file string.c, for an example of how to implement this using the callable library, and the general documentation

http://scip.zib.de/doc/html/cons__quadratic_8h.php#ad3707e7f7166bea83b7713cf2e52b0db

Have fun, ambros

Upvotes: 2

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