Re: My LP Formulation of the TSP: Conclusions

On Mar 25, 10:07 am, Patricia Shanahan <p...@xxxxxxx> wrote:
moustapha.di...@xxxxxxxxxxxxxxxxxx wrote:

...> 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.

...

As a programmer, I am interested in the process problems behind errors.
Suppose my program crashes because I got the wrong limit on a loop.
Obviously I need to fix that specific error. I also need to examine how
I decided on the loop limit, to see if the root cause of that error may
have affected other loops.

Until presented with a counter-example, you thought those constraints
were redundant. Do you understand what was wrong with your reasoning
about them? Could the same problem have affected anything else?

Patricia


Your question is reasonable. Leaving aside the issue of the validity
of the "counter-example" and focusing on the spirit of its
"construction" scheme, I found that I had erroneously assumed that the
flow balance of the z-variables would hold implicitly from the other
constraints of the model (excluding the "visit requirements
constraints" in question).

As I indicated in my earlier post, the current model contains a lot of
redundancies. But, it is *absolutely* "safe" in the sense that each
step of each proof follows very directly (without the need for any
constraint to hold implicitly).

....Call it excessive "over-kill". ...But as I said, "finessing" can
come later.

//MD


.

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