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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?

A.Omidi
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  • How did you calculate the LP value? Gurobi has the command m.relax() when you optimize this you get 63? – user3680510 Jun 05 '20 at 21:53
  • @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!!! – A.Omidi Jun 05 '20 at 22:01
  • 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. – user3680510 Jun 05 '20 at 22:31
  • @user3680510, I do that and the behaviour is the same!!! – A.Omidi Jun 06 '20 at 03:51
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    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. – T_O Jun 06 '20 at 09:45
  • @T_O, thanks, even though disabling the pre-solving, cuts and heuristics? I tried to use pure B&B algorithm. – A.Omidi Jun 06 '20 at 11:42
  • Can you share the lp file? – user3680510 Jun 06 '20 at 14:38
  • @A.Omidi: I think so. Have a look at Marco's answer in the question you mentioned. There, this happened due to strong branching. In the end, we will not be able to answer this for sure without knowing the implementation details of the solver. I guess, you have to accept that the LP relaxation and the MIP root node do not necessarily have the same value. – T_O Jun 07 '20 at 00:09
  • @user3680510, I will share ASAP. Thanks. – A.Omidi Jun 07 '20 at 11:42
  • @user3680510, please, see this .MPS file. – A.Omidi Jun 07 '20 at 21:00
  • @T_O, thanks. I think you would say the only way to get the LP relaxation valve is using a pure LP solver as Dr Lübbecke mentioned too. I checked the other solvers and some of them showed the LP relaxation equal to $63$. I would like to know, why some of the state-of-art solvers showed the different value and I think it may be a little confusing. – A.Omidi Jun 07 '20 at 21:02
  • yes i think the only reliable way is call the lp solver. i think they show a different value, because some solver are doing strengthenings which they might not consider to be presolve, but i am only speculating. the real reason i think can only a person from the solvers answer. – user3680510 Jun 07 '20 at 21:43
  • @user3680510, many thanks. – A.Omidi Jun 08 '20 at 03:45
  • I am not sure how GAMS interfaces with CPLEX but with CPLEX I get exactly the results you expect: If I do read Ex1.MPS, change problem lp, opt I get optimal value -63 for the LP problem. If I do read Ex1.MPS, set preprocessing presolve no, opt then I can see in the log that the root relaxation has objective -63. – Daniel Junglas Jun 09 '20 at 06:41
  • @DanielJunglas, many thanks for your response. I tried with GAMS(CPLEX, Gurobi, SCIP) and the results are the same. Maybe, this needs GAMS specific parameter than the solver parameters. I will check it again. – A.Omidi Jun 09 '20 at 08:32
  • @A.Omidi are you maximizing or minimizing? – Nikos Kazazakis Jun 12 '20 at 09:02
  • @NikosKazazakis, I'm trying to maximize. – A.Omidi Jun 12 '20 at 09:28
  • @A.Omidi Thanks. Are you using AMPL/PYOMO by any chance? If so, is there a constant in your objective that is equal to 4? – Nikos Kazazakis Jun 12 '20 at 11:43
  • @NikosKazazakis, thanks. I don't use AMPL/PYOMO. I'm using GAMS(CPLEX, Gurobi, SCIP) and SCIP optsuite and the results are the same. No, there isn't a coefficient equal to $4$ in the objective function. You could try the .MPS format of the problem in the above comments. Thanks once again. – A.Omidi Jun 12 '20 at 20:29

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