Re: Discussion regarding Mr. Diabys algorithm


moustapha.diaby@xxxxxxxxxxxxxxxxxx wrote:
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.

no :)

You have no "hard" restriction for this case, and you only *claim* that
combination of these restrictions can avoid it. But looking into
details - your belief is based on thinking "in *symmary* this
restrictions cut-off any non-legal flows" - but there is sum operation,
and we said that sum can be easily decieved.

Please point out ONE constraint that would cut of such variables:
z_5_5_6_6_6_7_7_7_8
z_5_5_6_6_6_7_8_8_9
z_5_5_6_6_6_7_9_9_8
....

If you claim that in summary of some restrictions combinations it may
be avoided... then let me tell you - it is FALSE.

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.

Yes it is. Maybe you didn't mention to nest anything but taking
perspective form y_isj_*** this *** is nothing else then some x_upv
model. Even if you don't store part of this model for p<s. Same with z.
If you think from perspective of z_isj_upv_*** then *** is nothing more
then x_krt model...

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.

And it isn't true. Your implication states:

there is z_isj_upv_krt>0 then there is set of TSP tours going through
isj, upv and krt - that is ok. But when you take different
z_i2s2j2_u2p2v2_k2r2t2 then you have to say that through this three
arcs there is some set of TSP tours... But you dont prove that these
sets are equal. That is what I have written before - your propositions
apply only to parts of TSP tours "seen" by variables - they do not
apply for whole (from beginning to end) TSP tours. And only way for you
to make it beginning to end thinking is sum based - but if sets of
tours "seen" by some variables differ from tours "seen" bu others but
this two sets sum-up to same value then your model is decieved... And
my construction shows it undoubtly!

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.

Wait a second... I'm objector here :). I have given you construction
feasible for BLP model which has better value then optimal TSP tour
what is best ever proof that your algorithm isn't capable of solving
large instances... What else do you need? You are only person who don;t
want to understand and accept it!

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.

It is only you who thinks so!

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.

I did! It is hard to solve it for any 32 instance, but remember that I
have designed flows "by hand". Then I was able to run 32^9 example
skipping zero-valued variables. And the outputs are avaliable - I have
already provided links to them in my paper!
- every non-zero variable form 32^9 is in variables_z.zip
- every equation containing *at least* one non-zero variable is in
equations.zip

Omited are equations like this:
a+b+c-d-e-f=0 for a=b=c=d=e=f=0

Do you think that adding 2^32 equations like this would change
anything? They are zeros at both sides!

This means that it *perfectly* fits to your model!

Best regards,

Radek Hofman

.

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