<br><font size=2 face="sans-serif">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.</font>
<br>
<br><font size=2 face="sans-serif">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.</font>
<br>
<br>
<table width=100%>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">From:</font>
<td><font size=1 face="sans-serif">"Kampas, Frank" <fkampas@wamsystems.com></font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">To:</font>
<td><font size=1 face="sans-serif">"hela masri" <masri_hela@yahoo.fr>,
<coin-discuss@list.coin-or.org></font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">Date:</font>
<td><font size=1 face="sans-serif">09/10/2009 09:37 AM</font>
<tr valign=top>
<td><font size=1 color=#5f5f5f face="sans-serif">Subject:</font>
<td><font size=1 face="sans-serif">Re: [Coin-discuss] multiple solutions
for LP</font></table>
<br>
<hr noshade>
<br>
<br>
<br><font size=2 color=#004080 face="sans-serif">One approach I’ve used
with other optimizers is to </font>
<br><font size=2 color=#004080 face="sans-serif">run the optimization,
</font>
<br><font size=2 color=#004080 face="sans-serif">convert the objective
function to an equality constraint equal to the objective function value,
</font>
<br><font size=2 color=#004080 face="sans-serif">create a new objective
function,</font>
<br><font size=2 color=#004080 face="sans-serif">optimize over and over
again with max iterations equal to one.</font>
<br><font size=2 color=#004080 face="sans-serif">Each optimization will
give you new solution with the original objective function value.</font>
<br><font size=2 color=#004080 face="sans-serif">It won’t give all the
degenerate solutions but will give some of them.</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 face="Tahoma"><b>From:</b> coin-discuss-bounces@list.coin-or.org
[</font><a href="mailto:coin-discuss-bounces@list.coin-or.org"><font size=2 face="Tahoma">mailto:coin-discuss-bounces@list.coin-or.org</font></a><font size=2 face="Tahoma">]
<b>On Behalf Of </b>hela masri<b><br>
Sent:</b> Wednesday, September 09, 2009 6:39 PM<b><br>
To:</b> coin-discuss@list.coin-or.org<b><br>
Subject:</b> [Coin-discuss] multiple solutions for LP</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman">I'm using CoinMp to solve some
linear programs.<br>
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.<br>
I used to use GetAndCheckSolution() <br>
<br>
Thank you,<br>
Hela Masri</font>
<br><font size=3 face="Times New Roman"> </font>
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