Originally posted by: Mintch Zulitch

Hi everyone,

First of all I want to apologize if my question would be too general, but I googled my question in every possible form and didn't come up with an acceptable answer.

My question is:

Does CPLEX support these two algorithms?

Branch-and-Price

Branch-and-Cut

If yes, to what degree? I mean: Are they fully implementable in CPLEX?

And where can I find sample files regarding these algorithms?

(Please note that the CPLEX mainly uses the branch-and-cut to solve MIP problems, and I know that!)

CPLEX does not really support Branch-and-Price since it does not support creating new variables during the search. To some amount you can work around that, see for example cutstock.cpp example in the distribution or several posts in CPLEX Forum. But if you want a real and full-blown Branch-and-Price then CPLEX does not support that. You could of course use CPLEX to solve the sub-problems, but the tree search would be up to you.

Since you already know that CPLEX uses branch-and-cut for MIPs, I am not clear what you are asking about branch-and-cut. Can you please be more specific?

Originally posted by: Mintch Zulitch

Very thanks for your answer,

Branch-and-cut is a generalization of branch-and-bound where, after solving the LP relaxation, and having not been successful in pruning the node on the basis of the LP solution, we try to find a violated cut. If one or more violated cuts are found, they are added to the formulation and the LP is solved again. If none are found, we branch.

The cut-generating procedures are classified as follows:

General purpose
Relaxation
Problem specific

I know what branch-and-cut is. But since you said you knew that CPLEX uses branch-and-cut to solve MIPs, I wonder what you meant by asking whether CPLEX supports branch-and-cut? Obviously it does, since it uses that to solve MIPs.

Originally posted by: Mintch Zulitch

Actually, I want to handle the the cut-generating process manually. At any arbitrary node, I apply my own cut.

In CPLEX this can be done using a user cut callback, see for example here.