SCIP: How to resolve LP after catching a 'node infeasibility' event,

Question

I have a working column generation algorithm in SCIP. Due to specific constraints that I include while generating columns, it might happen that the last pricing round determines that the root node is infeasible (by the Farkas pricer of course).

In case that happens, I would like to 1) relax those specific constraints, 2) resolve the LP, and 3) start pricing columns again.

So, I have created my own EventHandler class, catching the node infeasibility event:

SCIP_DECL_EVENTINITSOL(EventHandler::scip_initsol)
{
    SCIP_CALL( SCIPcatchEvent(scip_, SCIP_EVENTTYPE_NODEINFEASIBLE, eventhdlr, NULL, NULL));
    return SCIP_OKAY;
}

And, corresponding, the scip_exec virtual method:

SCIP_DECL_EVENTEXEC(EventHandler::scip_exec)
{
  double cur_rhs = SCIPgetRhsLinear(scip_, *d_varConsInfo).c_primal_obj_cut);
  SCIPchgRhsLinear (scip_, (*d_varConsInfo).c_primal_obj_cut, cur_rhs + DELTA);

  return SCIP_OKAY;     
}

Where (*d_varConsInfo).c_primal_obj_cut is the specific constraint to be changed, DELTA is a global parameter, and cur_rhs is the current right hand side of the specific constraint. This function is neately called after the node infeasibility proof, however, I do not know how to 'tell' scip that the LP should be resolved and possible new columns should be included. Can somebody help me out with this?

Answer 1

When the event handler catches the NODEINFEASIBLE event, it is already too late to change something about the infeasibility of the problem, the node processing is already finished. Additionally, you are not allowed to change the rhs of a constraint during the solving process (because this means that reductions done before would potentially be invalid).

I would suggest the following: if your Farkas pricing is not able to identify new columns to render the LP feasible again, the node will be declared to be infeasible in the following. Therefore, at the end of Farkas pricing (if you are at the root node), you could just price an auxiliary variable that you add to the constraint that you want to relax, with bounds corresponding to your DELTA. Note that you need to have marked the constraint to be modifiable when creating it. Then, since a variable was added, SCIP will trigger another pricing round.

Answer 2

maybe you should take a look into the PRICERFARKAS method of SCIP ( https://scip.zib.de/doc/html/PRICER.php#PRICER_FUNDAMENTALCALLBACKS ).

If the current LP relaxation is infeasible, it is the task of the pricer to generate additional variables that can potentially render the LP feasible again. In standard branch-and-price, these are variables with positive Farkas values, and the PRICERFARKAS method should identify those variables.