Solving integer programs with a few important binary gub constraints

During a branch and bound search of an integer program, decisions have to be taken about which subproblem to solve next and which variable or special ordered set to branch on. Both these decisions are usually based on some sort of estimated change in the objective caused by different branching. When the next subproblem is chosen, the estimated change in the objective is often found by summing the change caused by changing all integer variables with non-integer values, as if they were independent. For special ordered sets the estimation is done for each set as a whole. The purpose of this paper is to report some results from trying to do a simultaneous estimation for all the variables in a binary gub constraint. By this, the analysed problems contain one or a few constraints saying that the sum of n bindary variables should be equal to m(¸<n).