[Scip] Transformed variables

[Stefan Wiesberg]

Dear SCIP community,

although the concept of transformed variables has already been
discussed, I still need to ask for your help on some remaining questions:

1) In the presolving step, every original variable x_i is replaced by a
transformed variable t_x_i. As far as I understand, some further
variables might be added to the transformed problem. Which possibilities
are there?

2) I've heard of so-called negation variables. Is it possible that a
transformed variable t_x_i is deleted, e.g., because it is replaced by
such a negation variable, or do they always co-exist?

3) Suppose that a^T x <= b (*) is a valid inequality on original
variables for my IP. Is the inequality that evolves from (*) by
replacing every x variable by its corresponding t_x variable also valid?
E.g., if  x_1 + x_2 + x_3 <= 2 is valid, does this imply that t_x_1 +
t_x_2 + t_x_3 <= 2 is valid?
Or equivalently: Does the real-world interpretation of the original
variables change during transformation? With "real-world interpretation"
I mean a statement like "x_i_j states whether object i is put into bin j".

Thanks a lot and kind regards
  Stefan

-- 
Stefan Wiesberg
____________________________________________________
AG Diskrete Optimierung
Institut für Informatik
Universität Heidelberg
Phone: 49 6221 54 5746
E-Mail: stefan.wiesberg at informatik.uni-heidelberg.de

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