Originally posted by: Amar-SQU

I am using CPLEX 12.6.1 callable library  to solve a LP model that has more than one optimal solution.  Is there a way I could extract all the basic optimal solutions i.e. the coordinates of all the vertices of the facet corresponding to the optimum?

Thank you for your help.

Amar

Originally posted by: BoJensen

Generating all optimal basic solutions is not a trivial task. Here's a couple of worthy reads on the subject :

http://orinanobworld.blogspot.dk/2013/01/finding-all-solutions-or-not.html

http://orinanobworld.blogspot.co.uk/2012/10/detecting-multiple-optima-in-lp.html

Now if you wish to choose between alternative optimal solutions and not generate all of them, then you might use an approach similar to what Tobias suggest here :

https://www.ibm.com/developerworks/community/forums/html/topic?id=77777777-0000-0000-0000-000014617924