Re: [Help-glpk] Skip preprocessing

[Andrew Makhorin]

> I know that the example has no feasible integer points, that is the
> point of the example. 

Unbounded integer variables cause some problems. For example, due to
finite precision sometimes it is difficult to determine whether a mip
instance is infeasible (like yours) or it has a huge integer feasible
solution. For this reason many mip solvers (not glpk) do not allow
unbounded integer variables. However, for instances that appear on
practice it is always possible to find eligible estimation for bounds of
all integer variables. Moreover, if you expect that in optimal point
some integer variable takes on a value greater than 100, in most cases
you may declare it continuous rather than integer, since the error will
be less than 1%.

> The problem is that due to the bug, glpsol never
> even attempts to try to solve the problem with the simplex method.

Glpk mip solver perform preprocessing first. The simplex method applied
later to find optimal solution to lp relaxation of the preprocessed mip.

>  I
> would like to be able to present this example to my students and let
> them use glpsol to try to solve it and explain what the problem may
> be, but since glpsol does not even get past preprocessing it is a
> little to hard to explain what the program does.

Sorry, glpk is not perfect. Why not to use the option --nointopt to
disable preprocessing?

> 
> What I can do is to change the lower bound on x1 to 0 instead of 1.
> Then glpsol reports that the problem has unbounded solution (when
> solving the initial LP-problem) and in the solution output it reports
> status "INTEGER UNDEFINED". This change seems to not trigger the
> preprocessing bug.