Hello, I need help in path planning from a Hamiltonian matrix with a condition that I visit each point only once with starting point known.

mat=[0,10,8,7,7;10,0,10,5,6;8,10,0,8,9;7,5,8,0,6;7,6,9,6,0] % C is a hamiltonian matrix containing relative distances

In this case the points are A,B,C,D,E and let A be the starting point. Now, from A, I can move to either D or E. So two different paths are possible. How do I write algorithm for this such that I compare the travelling distance for each path and choose with minimum travelling distance? I have code for the matrix with unique elements, but need help when there are more than 1 path is possible.

Note: the number of visiting points is a variable and I chose only 5 i.e A,B,C,D,E just to explain.

[Torsten]

Isn't this the "Travelling Salesman Problem" ?

[akash sonnad]

yes

[Torsten]

Each point can be reached directly from each other point for your case, i.e. there are no distances in your matrix "mat" that are infinity ?

[akash sonnad]

the infinities which you are referring are the zeroes, i.e the diagonal elements

[Torsten]

I thought they mean that the cost to reach point i from point i is zero.

But you say your graph is complete with costs unequal infinity for all edges ?

[akash sonnad]

thats's obvious. Travelling distance between point i to point i is zero

[Torsten]

Again the question: your graph is complete with costs unequal infinity for all edges ?

[akash sonnad]

yes

[Torsten]

Try this code:

https://de.mathworks.com/matlabcentral/fileexchange/13680-traveling-salesman-problem-genetic-algorithm

Best wishes

Torsten.

[akash sonnad]

Thank you