Re: [Help-glpk] Figure out the exiting variable after simplex iteration

[Andrew Makhorin]

> I am using a column generation scheme with the GLPK C API.  I need to
> get a deeper understanding of what is happening in my model.  When a
> variable enters the formulation/basis and is assigned a non-integer
> primal value, I'd really like to know which variable left the basis to
> understand why the entering variable isn't integer (ultimately in this
> model all variables will be assigned binary values).

If you introduce a non-negative variable into the model and then
perform re-optimization, there may be many pivots needed to the primal
simplex to reach the new optimum, so many variables may left/enter the
basis.

> Can anyone recommend a clean way to do this?

If you need to know what happens on the very first pivot, you may
limit the number of simplex iterations by 1.

>   I suppose I could keep
> track of all non-basic vars before each iteration and the see who was
> added to the set of non-basics after a non-int variable enters the
> basis.  That sounds like overkill maybe?  Right now, after each new
> column is added, I check if it's primal value is between 0 and 1.  If so,
> I print out information regarding each row containing that variable if
> that row is on its bound.  I thought this would provide some insight, but
> doesn't quite get me there.  Hence the question I'm posing now.

> I can provide more information/clarification if it's helpful.

Could you explain what exactly do you need? Are you trying to generate
columns in such a way that keeps integrality of the basic solution?


Andrew Makhorin