My question has to do with integer programming and having a code that helps a researcher derive cutting planes.
Has anyone written some code, potentially interactive, to generate and explain cutting planes for a user or student?
I would like to see something like WolframAlpha's explanation of how to do an integral, but instead of how to derive some useful cutting planes for an integer program.
For example, I would like to run input an optimization problem $$ \max \ \ c^\top x $$ $$ s.t. Ax \leq b $$ $$ x \in \{0,1\}^n $$
- Solve the LP relaxation
- If the LP relaxation is fractional, --> have a solver generate some cuts that remove the fractional LP solution --> then have the code explain how to derive these cuts.
I think that this could be both a useful learning tool for students as well as an exploration tool for researchers.
Ideally, a user would run this on small integer programs (maybe 10 variables) to get a sense of what useful cuts for their integer program are.
Robert Vanderbei has a Gomory Cutting Plane Tool here: https://vanderbei.princeton.edu/JAVA/pivot/gomory.html