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From: AST@postman.hibo.no (Alf P. Steinbach)
Subject: Re: Shortest path the other way
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Date: Fri, 24 Feb 1995 12:56:47 GMT
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Keywords: GA, TSP

In article <3i9qkg$qb@ow23.fwi.uva.nl> koops@fwi.uva.nl (Jeroen) writes:
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>From: koops@fwi.uva.nl (Jeroen)
>Newsgroups: comp.ai.genetic
>Subject: Re: Shortest path the other way
>Date: 20 Feb 1995 11:24:16 +0100
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>Keywords: GA, TSP
>jh@Germany.EU.net (Joerg Heitkoetter) writes:
>
>
>>				"To P or !P that's the question."
>>					-- unknown
>
>>In article <3hvb2b$3l1@ow13.fwi.uva.nl>, koops@fwi.uva.nl (Jeroen) writes:
>>|> The problem goes like this: I have a number of points and I want to
>>|> connect them all with lines, so that the sum of the length of the
>>|> lines is as short as possible.
>>Ok; so unless I got something completely wrong, you're searching for the
>>minimum spanning tree (MST); i.e., since the MST problem is defined for
>
>Well, not exactly. Wish it was that simple.
>
>>Unless, you forgot to tell us that you can create new nodes "on the fly"
>>anywhere between the original nodes--then, you're searching for the
>
>Yes, that is the case.
>
>>Anyway--as far as an encoding is concerned, nodes are either connected or not;
>>this can obviously be represented with a 1 and 0 in an adjacency matrix; you'll
>>only need the lower (or upper) triangular matrix; and an algortihms that
>>converts this trangular matrix to a string, and back; which is pretty
>>straight forward. (The creation of an adjacency matrix or an adjacency list
>>is also presented in [4]).
>
>So I guess the easiest way of coming to a solution is to have a number of
>branchpoints, make a MST between them and the original points, and define
>operators for deleting branchpoints, adding branchpoints (either totally
>random or close to original points) and some sort of crossover thing.
>Well, I'll try that than!
>
>Thanks!
>
>>-- 
>>Have fun,	-joke
>
>>====== ____                           ==  Jrg Heitktter
>>===== /      /   /   ___    ___  _/_ ===  Research & Development
>>==== /----  /   /  /   /  /___/  /  ====  EUnet Deutschland GmbH
>>=== /____  /___/  /   /  /___   /  =====  Emil-Figge-Str. 80, D-44227 Dortmund
>>==                                ======  Tel/Fax +49-231-972 -00/-1111
>
>>"We are what we repeatedly do. Excellence, then, is not an act, but a habit."
>>	--Aristotle
>
>
>--------------------------------------------------------------
>Jeroen Koops     |  'Nothing sucks
>koops@fwi.uva.nl |   like an Electrolux!' 
>--------------------------------------------------------------

Hm.  Is this some kind of Steiner tree question?  In that case, have you
tried the *soap bubble computer* technique for finding a near (locally)
optimal solution?  Simply represent your nodes by matchsticks or whatever
in some container, fill in some soap water, stir & shake.  Now the
boundaries of the bubbles minimizes (locally & approximately) the tree
you want.  Have fun!   :-)

Incidentally, the soap bubble computer performs this remarkable feat in
O(n) time!
