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Suggestions for miplib2010
derived from optimal control of opinion dynamics
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1. Content
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The archive contains files of the type

  roc<modelversion>_<no. of stages>_<no. of voters>.{zpl,lp,log}

(roc = Rambau opinion control) that model an optimal control 
in the deterministiv dynamic system given by bounded-confidence dynamics 
in a system of opinions [Hegselmann & Krause model].  Background
is contained in the incomplete draft

  roc.pdf

in the archive.

There are two model versions: I and II.
 I: modeling with many big-M-constraints
II: modeling with many configuration variables

Solutions are known for Model I for 11 voters up to 3 stages,
for Model II up to 6 stages that are provided in the
log files *.log.

For the first unsolved instances, cplex does not even
come close to a solution.

Therefore, I find the instance valuable.

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2. Mathematical speciality of the instances
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In my opinion, the difficulty, in particular to find feasible solutions,
comes from the following fact:

The only independent decisions are no-of-stages many continuous
numbers between 0 and 1.  The remaining variables, mostly binary,
depend on that decision.  That means, the MILP-solver can never
branch on independent decisions.

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3. Further reading
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The background is contained in roc.pdf.  The draft is incomplete and only
for the miplib2010 team.  Please, do not distribute this file.

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