Re: FindShortestTour Function- Roundtrip & Constructive Heuristic
- To: mathgroup at smc.vnet.net
- Subject: [mg123420] Re: FindShortestTour Function- Roundtrip & Constructive Heuristic
- From: Dana DeLouis <dana01 at me.com>
- Date: Tue, 6 Dec 2011 03:14:32 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hi. I may not understand your question, but you can add a "Method" to the calculation.
Here are some x,y points:
pts=Tuples[Prime[Range@10],2];
And the distance is:
FindShortestTour[pts] //First
249.954
A few extra seconds might come up with a better choice:
{len1, tour1} = FindShortestTour[pts, Method -> "SimulatedAnnealing"];
{N[len1], len1}
{241.8011097365331, 223 + 2*Sqrt[5] + 2*Sqrt[17] + Sqrt[37]}
ListLinePlot[pts[[tour1]], Mesh -> All, PlotLabel -> N[len1]]
About 1-2 minutes of calculation might find something even better.
{len2, tour2} = FindShortestTour[pts, Method -> "IntegerLinearProgramming"];
{N[len2], len2}
{240.77995987511002, 231 + 4*Sqrt[2] + Sqrt[17]}
ListLinePlot[pts[[tour2]], Mesh -> All, PlotLabel -> N[len2]]
Just for fun. The first graph started in the middle, and the second graph started from point 1.
If you would like to see the first graph start from 1 also, here is one idea:
We'll start from the same point as tour2.
start = tour2[[1]]
1
t = RotateLeft[tour1, Position[tour1, start] [[1,1] ] - 1];
ListLinePlot[pts[[t]], Mesh -> All, PlotLabel -> N[len1]]
= = = = = = = = = =
HTH
Dana DeLouis
Mac, Ver 8
= = = = = = = = = =
On Dec 1, 6:02 am, Chrissi87 <c.cur... at googlemail.com> wrote:
> Dear readers,
> I have two different questions, both belonging the "FindShortestTour"
> Funktion:
>
> 1. I refer to an example if the "FindShortesTour" Funktion,http://reference.wolfram.com/mathematica/ref/FindShortestTour.html,
> you can find it under "Method".
> The example:
>
> d = SparseArray[{{1, 2} -> 1, {2, 1} -> 1, {6, 1} -> 1, {6, 2} -> 1,
> {5, 1} -> 1, {1, 5} -> 1, {2, 6} -> 1, {2, 3} -> 10, {3, 2} ->10, {3,
> 5} -> 1, {5, 3} -> 1, {3, 4} -> 1, {4, 3} -> 1, {4, 5} -> 15, {4, 1} -> 1, {5, 4} -> 15, {5, 2} -> 1, {1, 4} -> 1, {2, 5} -> 1, {1, 6} ->
>
> 1}, {6, 6}, Infinity];
>
> In: {len, tour} = FindShortestTour[{1, 2, 3, 4, 5, 6},
> DistanceFunction -> (d[[#1, #2]] &)]
>
> Out: {6,{1,5,3,4,2,6}}
>
> I would like to know now, if it is possible to change the calculation
> in that way, that at the end of the tour the last point will also be
> the first point.Lets say I have to start at knot 1 and at the end of
> my tasks I have to return to knot 1. So it would be a travelling
> salesman problem, but with the shortest tour to visit all knot. I know
> there is a travelling salesman function but for me it does not work,
> because I want to use the different Algoriths (Or Opt, Creedy...)
> which one can use with the "FindShortestTour" Funktion.
>
> 2. My second question refers to the different Heuristics to calculate
> the Shortest Tour.
> There is a group (CCA, Creedy...) which is known in the literature as
> a Constructive Heruristic and there is a second group (Or Opt, Two
> Opt..) which are improvement algorithtms.
> When one calculates by hand a problem like this, one has to construct
> a tour with a constructive heuristic (most not very good) and then
> make it better with an Improvement heuristic.
> I guess Mathematika is doing the same. Still, it is possible calculate
> the problem tight from the beginning with an Improvement algorithm.
> My question is now, What is the constructive algorithm mathematika
> uses? I really would like to know this.
>
> Thank u in advace for all your help.