Re: Discussion regarding Mr. Diabys algorithm



On Nov 17, 5:02 am, "Radoslaw Hofman" <rad...@xxxxxxxxx> wrote:
Uzytkownik <moustapha.di...@xxxxxxxxxxxxxxxxxx> napisal w wiadomoscinews:1163756083.390932.8850@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

I don't agree. For y_isj_*** this *** is nothing more then nested x_isj
model. For z_isj_upv_*** is the same.

Then we can build such models for every z_isj_upv_*** that each of them will
be:
- incorrect (using many times same cities k,t where k,t are not equal to
i,j,u,v) - IS THERE ANYTHING TO AVOID IT??
- balanced - they will sum up to make y_isj_*** incorrect models

Yes, the combination of constraints 2.8 - 2.11, 2.14, and Lemma 1.


Look - your belief that this is correct is based only on thinking "sum of
nested sub models for z makes y being correct" - but sum (as I mentioned)
does not give you possibility to answer what was taken to sum...


There is nothing "nested". It is not only sums that are balanced in my
model. Resaon is the same as above.



The "formal proof" is Proposition 2. The proof of that proposition is
very detailed in my paper. Can you point out the flaw in it?Yes, I will repeat what I wrote previously. You even don't try to give
formal proof that:
forall b in BLP-feasible-solution exists T subset TSP-tours
overallCost(b)=combination(overallCost(T))

In prop 2 you have point ii) which as I assume is ment to be answer...
well - only thing you can find studying your structure is that there exists
a PART of TSP tour. But it does not prove that paths are complete from
beginnig to end of tour. For example in 2.28 - you assume that if
z_isj_upv_krt>0 then exists set of arcs for that levels. What I am pointing
out is that they may have nothing in common with TSP-tours. Where is the
proof in opposite direction - that combination of parts of TSP-tours joined
together cannot fit in model? THAT IS FLAW.


Prop 2 only establishes that there is certain pattern to feasible
solutions of my model. No more.
Ther implication, however, is that if this pattern does not exist in a
given "solution", then that "solution" cannot be feasible for the
model, and that applies to *your* constructs.


Expression 2.28 is not assumed. It follows from expression 2.26 and
constraints 2.8 as stated in the paper.


Sorry, I am not doing this - I use only integer values in my counter example
to avoid any computation errors!


I don't think this is "proof" of anything.


So, it may be more fruitful if you could point out the error(s) in the
theoretical developments in the paper, especially Propositions 2 and 3
that your construct contradicts directly.Well... I don't know how to make it more clear - IT ISN'T PROOF FOR MINE
OBJECTION!


I don't think you have offered any proof at all. I don't think you have
addressed my objections either.



You have to prove that if there is some set of arcs for z_isj_upv_krt then
each of objects in set is TSP tour (from beginning to end of flow!). Or if
there is some global set of TSP tours in BLP solution then you have to prove
that every set generated from z_isj_upv_krt is direct subset of this general
set. There are no proofs for that!



Everything is already in the paper as I have stated repeatedly.


PS. Have you ran counter-example? It was easier for you when you would
considered this... is there flaw there?

As I have indicated befotre, I do not have computing resources
available to me that can handle LP's with 32^9 variables. But,
apparaently, you do. If you are able to write out all the constraints
and variables and check constraints, etc., you should be able to run
the LP. So, I think you should go ahead and do so, and make your
outputs public when you are done.


//MD.

.

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