Re: My LP Formulation of the TSP: Conclusions

On Mar 29, 2:27 am, "Radoslaw Hofman" <rad...@xxxxxxxxx> wrote:
Uzytkownik <moustapha.di...@xxxxxxxxxxxxxxxxxx> napisal w wiadomoscinews:1174831042.904707.279270@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>After further checking, I found that in the absence of Constraints
>2.12 - 2.13 (of the previous version), the flow connectivity
> constraints on the y-variables *only* (i.e., Constraint 2.8) were not
> sufficient for one of the steps of Proposition 2
> (Specifically,Expression 2.28 in the proof) to always hold. Hence,
> constraints 2.12 - 2.13 were indeed not redundant in the previous
> version of the paper.

Could you tell us for what N 2.13 is not redundant? It is obvious that it is
redundant for n<10, so if you "discovered" (what I had written half year
ago) that it is not redundant, then tell us at what N.

The formulation is very "robust." So, even relaxations of it produce
optimal solutions in a lot of cases. That is why, we have to
ultimately rely on the mathematics of the situation.


Also you could invent simmilar to 2.13 - not even mentioned in your article
(simillar but not only for first, but for every "layer") - are they
redundant, so you do not include them (refer to my original counter-example
paper). We can also add variables a_(isj)_(upv)_(krt)_(lqm) or more
dimensions... why do you use only 3?

We should rely on the mathematics of the situation for the "why?'s".


In the revised version, the flow balance equations on the z-variables
(that I had assumed would implicitly hold in the previous version)
have been explicitly added. (It is easy to verify that these
constraints would also be violated for any solution produced using
Hofman's "construction" approach).

Wow... that is what was written by me half year ago (that after inclusion of
2.13 counter-example is invalid)... But you wrot that it is IMPOSIBLE to
check, so what happen that it is possible now?

The "spirit" of your "construction" scheme is destroyed in the final
model.


//MD

.

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