Travel Salesman Problem


#1

Hi Guys,

I am going to solve the Travel Salesman problem:

I wanna find out the shortest path to visit all cities in my site.
But… I don’t know even where to start for it… (I am able to find out
any distance between two cities.)

Any clue?
Arthur


#2

Start here:

http://en.wikipedia.org/wiki/A*_search_algorithm

Regards,


Robert A. Nogueira de Oliveira


Tribunal de Justiça do Estado de Sergipe
Graduando em Sistemas de Informação - UNIT
MSN: removed_email_address@domain.invalid

“Ausência de evidência não é evidência de ausência.” (Carl Sagan)

On Mon, Apr 27, 2009 at 9:46 AM, Arthur C. <


#3

Robert A. removed_email_address@domain.invalid writes:

  1. (*) text/plain ( ) text/html

Start here:

http://en.wikipedia.org/wiki/A*_search_algorithm

This algorithm finds shortest path from initial node to goal node. TSP
(Traveling SalesMan) is aobut visiting all nodes in a graph.

Solving the TSP problem is not one of these problems for which there
eists a well known best algorithm. It belongs to the class NP [1],
well actuall it is known to be NPC [2], but you have read the section
regarding “Solving NP-complete problems” I suggest you read something
about branch-and-bound algorithms[3], and eventually use the A* search
algorithm as part of your BnB implementation.

Jarl

Footnotes:
[1] http://en.wikipedia.org/wiki/NP_(complexity)

[2] http://en.wikipedia.org/wiki/NP-complete

[3] http://en.wikipedia.org/wiki/Branch_and_bound


#4

I said start here, no finish here :slight_smile:


Robert A. Nogueira de Oliveira


Tribunal de Justiça do Estado de Sergipe
Graduando em Sistemas de Informação - UNIT
MSN: removed_email_address@domain.invalid

“Ausência de evidência não é evidência de ausência.” (Carl Sagan)


#5

Thanks guys,

I kinda understood the basic idea of the TSP. i wanna do something like
heuristic functions. Or, something like:

http://www.ruby-forum.com/topic/127031#new

I don’t know if the “grid” method mentioned is applicable for general
TSP.

Thanks again.

Robert A. wrote:

I said start here, no finish here :slight_smile:


Robert A. Nogueira de Oliveira


Tribunal de Justiça do Estado de Sergipe
Graduando em Sistemas de Informação - UNIT
MSN: removed_email_address@domain.invalid

“Ausência de evidência não é evidência de ausência.” (Carl Sagan)


#6

Arthur C. removed_email_address@domain.invalid writes:

Thanks guys,

I kinda understood the basic idea of the TSP. i wanna do something like
heuristic functions. Or, something like:

http://www.ruby-forum.com/topic/127031#new

I don’t know if the “grid” method mentioned is applicable for general
TSP.

It is not. It is only applicable to the special case TSP (points are
on a euclidean grid) mentioned there. Secondly the method does not
find optimal solution. Both of these limitations are mentioned on the
web-page.

Let me remind you, if you find a polynomial time algorithm for solving
the general TSP problem, you have prooved that P=NP[1] and thereby
solved one of the seven millenium Prize Problems[2] and you will be
rewarded US$1,000,000. So get used to it: “There is no easy way”.

So my suggestion is to analyse what you really need to solve! your
problem may very well be a special case TSP, for which there is a
polynomial algorithm. Secondly in practise you may not need the
optimal solution, just a very good solution. Could you ellaborate on
your real problem.

If that is not the case and you really need to solve TSP. you may
investigate state-of-the-art implementations on
http://www.research.att.com/~dsj/chtsp/ (I belive most of them are
some kind of branch-and-bound algorithm), the page may seem old, but
as you may have guessed, TSP is not called a “millenium” problem for
nothing :slight_smile:

Jarl

Footnotes:
[1] http://en.wikipedia.org/wiki/P_=_NP_problem

[2] http://en.wikipedia.org/wiki/Millennium_Prize_Problems