[Coin-discuss] multiple solutions for LP

[Michael Hennebry]

On Thu, 10 Sep 2009, acw at ascent.com wrote:

> In fact, if you create the new objective function correctly, it should
> give _all_ the solutions.  The trick is to make it so that every solution
> has a distinct (new) objective.  Make the new objective function
> incorporate only the integer variables.  It should have the form x_0 + e

The OP doesn't have any integer variables.

> x_1 + e^2 x_2 + ... + e^(n-1) x_(n-1), where the x_i are the integer
> variables, and e is some transcendental number.  (The mathematical e would
> work, but might be too big.  Try sqrt(e) or e^(1/10) until you find a
> value whose (n-1)st power isn't too enormous.)  By definition, no two
> integer combinations of powers of a transcendental number are equal.
>
> Each time you find a solution, add a constraint parallel to the objective,
> that excludes that solution; the next pass will find the next one, and so
> on.
>
>
> From:
> "Kampas, Frank" <fkampas at wamsystems.com>
> To:
> "hela masri" <masri_hela at yahoo.fr>, <coin-discuss at list.coin-or.org>
> Date:
> 09/10/2009 09:37 AM
> Subject:
> Re: [Coin-discuss] multiple solutions for LP
>
>
>
> One approach I’ve used with other optimizers is to
> run the optimization,
> convert the objective function to an equality constraint equal to the
> objective function value,
> create a new objective function,
> optimize over and over again with max iterations equal to one.
> Each optimization will give you new solution with the original objective
> function value.
> It won’t give all the degenerate solutions but will give some of them.
>
>
>
> From: coin-discuss-bounces at list.coin-or.org [
> mailto:coin-discuss-bounces at list.coin-or.org] On Behalf Of hela masri
> Sent: Wednesday, September 09, 2009 6:39 PM
> To: coin-discuss at list.coin-or.org
> Subject: [Coin-discuss] multiple solutions for LP
>
>
>
> I'm using CoinMp to solve some linear programs.
> is there anyone who knows how can I check if the problem have multiple
> solutions, and in this case how to get the set of solutions.
> I used to use GetAndCheckSolution()

-- 
Michael   hennebry at web.cs.ndsu.NoDak.edu
"Pessimist: The glass is half empty.
Optimist:   The glass is half full.
Engineer:   The glass is twice as big as it needs to be."