[SCIP] MIP-start in SCIP

[Stefan Vigerske]

Hi,

it's difficult for me to follow what you're doing.
If there is some unexpected behavior with the mipstart option in 
GAMS/SCIP, then send me a model and data to reproduce the behavior, or 
at least some log files.

Stefan

On 26/06/2023 13:17, Abbas Omidi wrote:
> Dear support team,
> 
> I am working on a large-scale scheduling problem in order to compare the
> current resource capacity and the required one to maximize resource
> utilization. Let's say there exist more than 80 resources and around 250
> tasks that should be processed in the weekly duration. Also, all of the
> data and its limitations are already known in advance.
> 
> In the first step, I have tried to formulate the problem as a MIP. I
> managed to investigate around four different formulations. However, each of
> which has its limitations in the solving process. For example, the first
> and the second contain more than 11M rows and 10M variables. (9M are
> binary). The third and the fourth have a better situation with the aid of
> tightening formulation. They still have around 3M binary variables and 500K
> rows. Actually, neither SCIP nor CPLEX could not solve such a problem in a
> reasonable amount of time as we expected.
> 
> an approach I am working on is by producing as good an initial solution as
> possible and then feeding that into the solver. For that I write an
> optimization model, again a MIP, to capture some of the original problem
> limitations. The main variable in this auxiliary model is the same as the
> main variable in the original model. I can solve this auxiliary problem by
> a solver or by a heuristic method to invoke either an optimal or
> near-optimal solution respectively.
> 
> The strange behavior is here:
> When the auxiliary problem is solved, I fix the value of the variables as a
> MIP-start on the original problem. By that, the solver log shows the
> MIP-start cannot produce any incumbent. And the solving process continues
> as the usual paradigm that the solver decides. In the second attempt, I try
> fixing the original main problem variable bounds (LB and UB simultaneously)
> by the auxiliary problem output. In this situation, the strange thing is
> that the solver can find a very good initial incumbent at the early stage
> of the solving process, and also the solving time significantly decreases.
> 
> ---------
> P.S:
> The original problem contains mixed variables. The main is a binary, also
> auxiliary binary variables for interchanging relations, and some of the
> positive variables as intervals. In the auxiliary problem, there is a
> binary as the same as the original main binary variables. Also, the
> provided initial solution by the auxiliary problem covers all of the main
> binary variables in the original one, but not for the rest.
> 
> We managed to test some instances of the original problem, (already as
> small as possible so that we can track the behavior of the model and its
> solution), and actually with the practical data. In all of the cases, the
> solution of the original problem corresponds to what we were expecting.
> Also, by having the fixed main binary variables the outputs are the same as
> the original ones. I should still say, I mean by CPLEX and SCIP is by
> calling them into a third-party language, GAMS. However, I tried different
> MIP-start parameters in GAMS/SCIP, but it does not have any impact on the
> solving process behavior.
> ---------
> 
> 
> *I was wondering if, how is it possible the solver rejects an initial
> solution as a MIP-start, but accepts that after fixing the main variable
> bounds?*
> 
> 
> Thanks in advance
> Regards
> Abbas
> 
> 
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