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<p><font color="#0000FF">//// Danh, I just realized I only sent you a reply , but did not post it to the mailing list. So I am doing it now (I received your reply on my personal mail). /////</font><br>
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<font size="2">>> Hi all, I has an lp problem which has more than one solution, and I want to get all of them. Is there any way in Clp to do that? For example, this problem: min x + y subject to x + y >= 3 x >= 0 y >= 0 has two solutions (0,3) and (3,0) using the simplex method If I want to get to solutions, which function in Clp should I use?T hanks</font><br>
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<b><font color="#0000FF"> Hi!</font></b><br>
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<b><font color="#0000FF">I am just a user of CLP, so I only can give an approximate advise.</font></b><br>
<b><font color="#0000FF">In general the set of solutions to an LP problem is a convex polyhedron. This polyhedron can be as complex as the original feasible region. Thus in general describing the set of all solutions is hard. </font></b><br>
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<b><font color="#0000FF">But you can get several random solutions by randomly modifying the objective function by a small epsilon.</font></b><br>
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<b><font color="#0000FF">I.e. generate a random co-vector with coords in [0,1] , in your case (x0, y0). Add epsilon * (x0, y0) to the objective function: MIN (1 + 0.000001*x0) * x + (1 + 0.000001*y0) * y. Solve. You have a random optimal solution to the original problem{ x , y } . If your epsilon is small enough the solution is _EXACT_, not approximate (you only need to recompute the value of the original objective function) .</font></b><br>
<b><font color="#0000FF">Repeat as many times as you want to get more random solutions.</font></b><br>
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<b><font color="#0000FF"> - Alexey</font></b><br>
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----------------------------------------------------<br>
Dr. Alexey Lvov<br>
IBM T.J. Watson Research Institute<br>
1101 Kitchawan Rd. (Rt. 134) Office 34-159<br>
Yorktown Heights NY 10598<br>
Tel: (914)-945-3732<br>
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