Diskussion:Integer linear optimization: Cutting Planes 1

Approach

Your approach is really good. It is mathematical correct. Really good is your mathematical donation for the seperation between the integer fraction and the rest. To understand the problem it is really important to make clear that the rest must bie positiv and between 0 and 1, which you did very well.

Example

You chose a great and typical example to show the working of the cutting plane method. Your entire example is correctly solved and in every single step good enough explained. So it was easy to understand the method and follow your example step by step. Your graphics show what really happans in the cutting plane method and so it was not hard to learn the advanteges from the cutting plane method.

Criticism

First of all it is necessary to look at the references. Your references show a really good example, which helps a lot by understanding the work of gromorys cutting plane method, but it does not have a reference in itself. Additional to that there is not realy an information about the cutting plane method, it is only an (really good one) example.

It would be great if you get any information about every possible chase which can appear: what if there is no optimal solution? what if there are more than one optimal solution? But we were faced with the same problems and know that it would expand the wikientry to much, so we did not work that out, too. With exactly the same reason we did not explain other cutting-plane-methods like the directly cutting plane method from gromory- so did you.

The last and at least important point. In your first part you have a grammaticle mistake: "...so that after cutting the feasible region finally we actually the get integer solution." Perhabs it would be enough by switching "the" and "get".

Nice job, specially your graphics which makes the complexity of the problem way better to understand and the mathematical approach!

Comment by:

Thomas Wagemann

Marcel Hotzelt

Sandra Born