[Osi] How to define SOS constraint

[Christian Schmidt]

Hi John,

> There are many reasons why replacing integer variables with SOS can
> degrade performance.

That is very surprising to me, because to replace a SOS constraint with 
binaries I need to use the "Big-M" method:

SOS: x1, ..., xn <= 1

<=>

forall_i xi <= M yi
sum_i yi <= 1
y1, ... , yn: binary

At least from theory Big-M should produce bad relaxations.

> a) Cut generators don't work.
> b) Most heuristics don't work
> c) Can take longer to get good solutions due to branching strategy.
> d) Fast Clp based mini branch and bound doesn't work with SOS.
>
> For a) and b) what you can do is leave variables as integer but add SOS
> - see sos.cpp.  The sample program did not use a) or b) anyway.

I did not use any special cut generators oder heuristics knowingly. I 
simply adapted your raw example in sosTest.cpp by using the 
OsiCbcSolverInterface's getModelPtr to add CbcSOS - so a) and b) should 
not be the cause, right?

> If you were comparing to standalone solver then it is not surprising
> performance suffered. You could try moving some of sos/sosTest into
> an example like driver4.cpp to use standalone solver.

The problems I need to solve are large linear models (1000's of 
constraints, 100'000's of variables - multicommodity networks flows with 
some linear side constraints) except for a few SOS1 constraints. I might 
add SOS2-constraints in the future, but besides that I don't have any 
integer variables.

> Other possibilities are three way branching objects if c) is a problem.

Could you clarify this? Example?