[Coin-discuss] multiple solutions for LP

[acw at ascent.com]

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 
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() 

Thank you,
Hela Masri
 
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