Re: Discussion regarding Mr. Diabys algorithm


Uzytkownik <moustapha.diaby@xxxxxxxxxxxxxxxxxx> napisal w wiadomosci
news:1163756083.390932.8850@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

No, the error you are making here is you are assuming constraints work
in isolation. I am not "thinking" anything. I am relying on the
mathematics in the paper, particularly, Proposition 2.

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

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...

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.

When "playing" with sums (and your model summarizes flows) it is
difficult
to trace what was taken to sum.

I perfectly agree with this. That is why we must rely on mathematics
instead of computer codes and untested, ad-hoc procedures as you do.

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

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!

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!

Best regards,

Radek Hofman

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


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