[SCIP] advice sought on solving strategy

[James Cussens]

Hi all,

I'm looking for some advice on how to implement a particular solving strategy.

I have a problem where there are two set of (binary) variables. One set, call it Q, has a quadratic number of variables, the other set,
call it E, has an exponential number of variables. The variables in E are actually products of those in Q and only variables in E
have non-zero objective coefficient. In my current strategy all Q variables and a reasonably small subset of E variables are created initially and
further E variables are priced-in later (if necessary).

In the sort of problems I'm aiming to solve, the user may well want to impose constraints on the variables in Q. I would like to use these constraints to
speed up the creation of the initial set of E variables. I'm thinking of an approach like this:


  1.
Create Q variables
  2.
Read in user constraints on the Q variables, if any
  3.
Propagate these constraints (perhaps with several rounds) and (hopefully) produce fixings for some of the Q variables
  4.
Use any fixings to speed up the creation of initial E variables. (They will also be used, of course, in any future pricing.)

I'm not sure how best to implement this. I could call presolve after step 2 but perhaps SCIP will just solve the problem at that point unless I somehow flag
that some E variables are on their way. I think I am looking to do propagations at step 3 and nothing else.

James

James Cussens
Room MVB 3.26
School of Computer Science, University of Bristol
Phone: +44 (0)117 455 8723
https://jcussens.github.io/
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