[SCIP] The difference in solution between SCIP and Gurobi

[Ambros Gleixner]

Hi Shinji,

You are right that SCIP and Gurobi are both branch-and-bound solvers and 
that they will give you (within numerical tolerances) exact results. 
However, since branch-and-bound is an exponential algorithm in the worst 
case, they do not always converge to the optimum, in particular for hard 
problems.  If they do not converge, you get a primal bound for the best 
solution found and a dual bound with the promise that there can be no 
better solution than the dual bound.  The exact objective value can lie 
anywhere in this interval.

What you observed is probably that Gurobi converges faster than SCIP and 
so within your time limit you see a worse primal bound.  This is not 
uncommon.

By changing SCIP parameters you have already started to try and tune 
SCIP to converge faster.  MIP solvers employ many different tricks 
internally and most likely you can find improved parameters for your 
problem.  A look at the log file and the statistics at the end can aid 
you in identifying which parameters to look at.  The interactive shell 
tutorial at scipopt.org/doc contains some basic examples for that.  Hope 
that helps getting started.

Best,
Ambros



Am 21.07.2023 um 10:33 schrieb 佐藤信治:
> Hello, SCIP experts,
> 
> I have a question about the difference between SCIP and Gurobi. SCIP and 
> Gurobi are each B&B (branch and bound) solvers, and I expect that both 
> will give me exact solutions (if I spend enough time). However, Gurobi 
> gives better results than SCIP when solving difficult problems in my 
> environment, and I don't know why. If I set the "max/restarts" parameter 
> of SCIP to 0 to prevent restarts from occurring, I get a slightly better 
> solution, but it is inferior to Gurobi's solution. What is the reason 
> for this difference in solutions? Also, is there any way to get a good 
> solution like Gurobi with SCIP, even if it takes longer?
> 
> 
> Maybe my English is strange.
> 
> Thank you very much !
> 
> ===========================================
> Shinji Sato, The University of Electro Communications
> 
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