[SCIP] A specific question about the Graph Coloring Application

[Yunzhuang Shen]

Hi SCIP Team,

I am doing research about Branch-and-Price, using the code of the Graph Coloring Problem provided in the SCIP applications folder.

In `pricer_coloring.c', lines 717-725 are for updating the lower bound using the Lagrangian bound of the current LP to my understanding.

However, The equation for computing the Lagrangian bound seems to be incorrect. Specifically, why the primal bound is used to multiple by the reduced cost?
SCIPgetLPObjval(scip) + ((1.0 - max_obj) * SCIPgetPrimalbound(scip))

However, the Lagrangian bound to the current RMP seems to be simply the optimal LP objective value of the current restricted master problem plus the optimum of the current pricing problem.

I would like to confirm this with you either this is a typo or I misunderstood something.

Regards,
Yunzhuang

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