Re: My LP Formulation of the TSP: Conclusions


Uzytkownik <moustapha.diaby@xxxxxxxxxxxxxxxxxx> napisal w wiadomosci
news:1175165597.236162.220620@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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.

Ok, so you are going to show us some mathematics now? There is no
"mathematics" in you paper...

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.

No... :)
If you let us all source codes of your program then I shall show you CE for
your model with 2.13 :)

BTW: I still cannot understand why are you refusing to think about these
facts:
A. for polytope with 2^n vertexes there are O(2^n-1) facets
B. having O(n^7) (or even O(n^15)) restrictions it is IMPOSSIBLE to "cover"
every facet
C. if facet is not covered by restriction, then target function "paralell"
to this facet will give incorrect result

It works even in 2D! Consider example: generate 2^n points fulfilling
(x-3)^2+(y-3)^2=1. Now you are trying to convince us that your linear model
containing O(n^c) lines will produce ALWAYS for ANY POSSIBLE TARGET FUNCTION
correct solution (correct distance between zero and nearest point from
generated solution set). It is obvious that it is not true! See example
http://www.teycom.pl/diaby/eq2.png

Why then having complicated multi-dimensional structure you claim to have
model "covering" any possible of O(2^n-1) facets? You do not know how this
structure "looks like" for n=100 because it is impossible to generate all
vertexes and check if you model is still correct. Unless you prove (using
mathematics) that number of facets is polynomially bounded untill your model
cannot be considered as correct.

Radek Hofman


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