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Dynamic Programming solution to the TSP



This function solves the Traveling Salesman Problem (TSP) using Dynamic programming (DP).

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The function is based on the paper by Held and Karp from 1962. The DP is guaranteed to provide the accurate (optimal) result to the TSP, but the time complexity of this algorithm is O(2^n n^2), which limits the use of this algorithm to 15 cities or less.

NOTE: For reasonable runtime, please do not try to calculate a tour of more than 13 cities. DP is not for large sets of cities.

MATLAB release MATLAB 7.6 (R2008a)
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Comments and Ratings (8)
07 May 2015 zhang zhaozhi


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17 Nov 2012 Thanapan  
19 May 2012 Leonardo BOrges

Cool i need this solutions for my study academic, thak you

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22 Feb 2012 Vahid

Vahid (view profile)


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22 Feb 2012 Elad Kivelevitch

As I said, I haven't tested it for an asymmetric TSP. You will need to pass a list of cities with n rows and 2 columns. This list will not be used in calculating the Dmatrix, but will be used for knowing the number of cities.

You know, it's a MATLAB code that you could modify and try to run your own versions...

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22 Feb 2012 Vahid

Vahid (view profile)

If I put an assymetric Dmatrix, what should I put as the cities coordinates?

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14 Feb 2012 Elad Kivelevitch

Correct. Just a symmetric TSP and only for a limited number of cities.

However, now that I think about it, I have no idea what happens if you use an asymmetric Dmatrix. Maybe it will work. Try it sometime.

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14 Feb 2012 Vahid

Vahid (view profile)

Thanks for the code. Is is only working for symmetric TSP?

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