[Scip] Branch and Bound Bi-objective

[Gregor Hendel]

Dear Emmanuel,

sorry for the late reply. The use of customized relaxations requires the 
implementation of a relaxation handler. A quick starting guide on how to 
do this can be found in our HowTo section on relaxation handlers 
<http://scip.zib.de/doc/html/RELAX.php>.

The crux is, of course, how to handle additional objective coefficients 
for every variable. This can be currently managed, eg, by entering 
diving mode of SCIP, changing all variable objective coefficients, and 
resolving the diving LP.
Your relaxation should then also have a mechanism to store every node's 
lower bound according to the
additional objective.

As far as I know, multiobjective problems are usually solved as a series 
of weighted combinations of the objective functions. The generation of 
such a sequence is easy to achieve by changing the objective coefficients
for all variables, and resolving the problem with SCIP. (Since primal 
solutions stay feasible, you might consider transferring them from one 
solving round to the next, as well).

If everything works as planned, the next SCIP release will contain more 
refined reoptimization techniques and a multiobjective solver as an example.

Hope this helps,
Gregor

Am 11.03.2015 um 15:54 schrieb Emmanuel Kieffer:
> Hello,
>
> I would like to know if it is technically possible to use SCIP to
> perform a Bi-objective Branch and Bound?
> If yes, I need to solve several relaxed problem at each nodes. So far I
> know, it's possible to deactivate the standard LP relaxation and use a
> custom one but how is it work?
>
>
> Thank you
>
> Best regards,
>
> Emmanuel
>
>
>
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