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(I apologize. I saw this question but, I do not know these may be the same or not.)

I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective value about $63$ but, when the problem is solved by MIP solvers like CPLEX, Gurobi and SCIP, the relax solution is reported $59$. (even though I disable pre-solving, cuts and heuristics).

Root relaxation: objective 5.900000e+01

In all of the cases, the value of the variables are the same and the problem is solved optimality.

I was wondering if, is there any way to get the root relaxation value equal to $63$ by using MIP solvers or this is an advanced technique in which the solvers use to speed up the solving time?

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  • $\begingroup$ How did you calculate the LP value? Gurobi has the command m.relax() when you optimize this you get 63? $\endgroup$ – user3680510 Jun 5 at 21:53
  • $\begingroup$ @user3680510, thanks. I'm using GAMS and the syntax for solving the LP relaxation is rmip. By using this you could get the value of the root node and it is $63$ but, by setting the syntax to mip the value is $59$. I think the value of the root node in LP relaxation or MIP directly should be the same but those are different!!! $\endgroup$ – A.Omidi Jun 5 at 22:01
  • $\begingroup$ I would try to write an lp file and read in this file directly into the solver and see if this behaves the same way. $\endgroup$ – user3680510 Jun 5 at 22:31
  • $\begingroup$ @user3680510, I do that and the behaviour is the same!!! $\endgroup$ – A.Omidi Jun 6 at 3:51
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    $\begingroup$ Please keep in mind that in a MIP, more preprocessing etc. can be done than in an LP. Thus, the MIP root node can be stronger than the LP relaxation. $\endgroup$ – T_O Jun 6 at 9:45

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