Shortest path through nodes

Hi everyone,

In a 2D plane I've got a starting point and a finish point.

Let's say they are:

p1_xy = [0 1];
p2_xy = [9 8];

Besides those two, I have another bunch of points:

P = [1 1 ; 2 1 ; 3 2 ;  3 3 ; 3 4 ; 5 6 ; 7 6 ; 8 8 ; 8 9];

Is there a simple strategy to find the shortest path from p1 to p2 passing through all P nodes just once?

I think it's some kind of mathematical process. I've found something, but something too complex for my purposes; maybe there's some useful simple function that I don't know about

Thanks to anyone who wants to help me!

[Bjorn Gustavsson]

Well, no.

This is a version of the traveling salesman problem, which is notoriously difficult, see: Traveling-salesman problem. If you have a small enough bunch of points to pass it is not too bad to solve. Matlab has a (old!) demo of the travling-salesman problem try it:

travel

Otherwise your best bet is the seemingly complex solutions you can find.

Answer 1

[Christine Tobler]

As Bjorn mentioned, this is the traveling salesman problem. The optimization toolbox has an example of how to use their intlinprog solver to solve such a problem: https://www.mathworks.com/help/optim/examples/travelling-salesman-problem.html