[SCIP] The difference in solution between SCIP and Gurobi

[佐藤信治]

Thank you for replying. I ran the SCIP solver with limits/gap=0 and Gurobi and so on for about a day. The result was that Gurobi gave a better solution than SCIP. It is also clear that the Gurobi solution is not included in SCIP's dual gap and primal gap. This is puzzling, given that SCIP gives a range of optimal solutions. What is the reason for this? Could it be that the problem I am dealing with is numerically unstable?
Thank you.



==========================
Shinji Sato

> 2023/07/23 5:59、Ambros Gleixner <gleixner at zib.de>のメール:
> 
> 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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