[Cbc] Is there a way to find the "closest" integer solution to a relaxed solution?

[Ted Ralphs]

Hi Jonathan,

I can think of a number of reasonable ways of modeling this problem, so
you'll have to determine what is best for the application. Most
straightforwardly, you could take your objective function to be the
distance of the solution from the target. To formulate this mathematically,
distance would have to be defined in terms of a specific norm. The
difficulty of solving the resulting problem would then depend on what norm
was chosen. It may or may not be possible to solve such a problem with Cbc
itself.

Alternatively, you could also consider searching for the best point
according to some other objective in some neighborhood, such as the set of
all solutions that are obtained by rounding the values in your given
solution up or down. This could be formulated as in integer program and
solved with Cbc.

Cheers,

Ted

On Thu, Nov 2, 2017 at 12:54 AM, Jonathan Lee <jonathan.lee.975 at gmail.com>
wrote:

> I have an integer program whose objective is to be as close as possible to
> a non-integer solution that I already have ("close" defined below). Is
> there any way I can guide Cbc to search near that solution? I've looked
> into CbcCompare and CbcHeuristic, but the documentation and examples
> haven't been helpful.
>
> By way of explanation, suppose I had a model with two integer variables x
> and y. I want (x,y) to be "as close as possible" to (2.7, 5.2). So (3, 5)
> would be best and I want to check there first. Then, I guess,
> (2,5),(3,6),(2,6), etc.
>
> Strictly speaking, the "target" solution I have is basically the average
> value that each variable takes (over all solutions). I want an integer
> solution that would appear to have been drawn from this distribution (say,
> by passing a chi-squared test).
>
> Thanks for any help
> --Jonathan
>
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>


-- 
Dr. Ted Ralphs
Professor and Interim Department Chair
Industrial and Systems Engineering
Lehigh University
(610) 628-1280
ted 'at' lehigh 'dot' edu
coral.ie.lehigh.edu/~ted
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