# Can presolve reductions change the value of the linear programming relaxation?

For integer programs solvers (like Gurobi, Cplex, ...) report the value of the linear programming relaxation for integer programs, i.e.

Root relaxation: objective 2.648400e+02, 233 iterations, 0.01 seconds


Is this value independent of the presolve reductions? Is this value always the same for all solvers/versions (if we ignore numerical problems)?

the answer is even worse than "no"; I recently used SCIP to compute an LP relaxation, and the outcome (the value of the dual bound) depended on the branching rule I activated (even though I never branched!).