How to obtain root node dual bounds

In its default mode, GCG performs an automatic Dantzig-Wolfe reformulation to solve a problem. A key reason to perform a DW reformulation is a stronger dual bound obtained from the LP relaxation of the DW master problem.

During the solving process, GCG will output the latest dual bound. However, the reported dual bound is not necessarily identical to the bound obtained from the LP relaxation. This is due to internal optimizations in SCIP and GCG which have an impact on the dual bound.

Obtaining LP relaxation of root node

The following settings can be used to obtain the LP relaxation of the root node:

set limits nodes 1
set sepa emphasis off
set pricing masterpricer advanced abortpricingint FALSE

These parameters result in GCG (1) solving only the root node, (2) not including cuts in the master and pricing problems, and (3) not aborting column generation before the restricted master problem is optimal.

After solving the problem with optimize, the reported final dual bound is the objective function value of the LP relaxation of the restricted master problem.

GCG

Table of Contents

How to obtain root node dual bounds

Obtaining LP relaxation of root node