Sunday, March 15, 2009

Fixed LP after MIP

Hi everybody,

After I solve a problem as an IP, I fix some of the variables
(complicating ones) to integer values of optimal solution to the IP
and solve the problem as a LP. The objective function only depends on
the fixed variables in both problems and there are constraints which
will be binding also those that will not. The problem is highly
degenerated.

The problem now is that I can not get any non-zero values for dual
variables using getDual or getDuals.

Anyone likes to put a comment on?

Cheers,

GAMS does this with all its MIP solvers to produce marginals for the rows and columns.

At the end of your fixed LP you should have a complete basis with m basics and n−m non-basics. The (non-binding) rows are likely to be basic, hence your zero's. The fixed integer variables are likely to be non-basic at bound, so you should see some nonzero marginals there.

I am sure your solver can produce a solution listing or a basis file so you can have a look where the non-basics end up and their marginal value (the dual value or reduced cost).