Forum Discussion
Is there any example of combination of Benders Decomposition and Column Generation?
Dear all,
I would like to know if there is any example (with code) of the combination of benders decomposition and column generation. I know that there are already some examples for column generation and for benders decomposition. However, I am looking for an example of the combination of the two problems.
If there is no such example, can you please provide some explanation of how to combine the two models?
Thank you all for the help
Bests,
2 Replies
Dear Francesco,
I'm afraid there is no such example in our distribution. Combining the two techniques requires a specific application that can benefit from it, and is anyway very application-dependent. For instance, how are both modeling techniques useful for the application? Is there a subset of variables that allows for decomposition? And is there a way of modeling the problem that implies an exponential number of variables? If this is the case, I suppose a combination of the two techniques can be useful.
While the Benders Decomposition would require you to set up callbacks for the branch-and-bound, the column generation does not, in general, require defining callbacks as it can be carried out in a single loop, as long as this is done before the branch-and-bound. If you envision doing column generation within the branch-and-bound, things get a lot more complex as you need branch-and-price.
Hope this helps. Regards,
Pietro
Thank you very much for your help.
Bests,
Francesco
