Shortest path between start and end point with many other points in between

Sorry if double post, but I haven't found this specific problem in the search function. I want qgis to show me the shortest path (direct) between many points with each point only is hit once. There is also a start point and an end point.

So that it looks like this (just an example and obviously NOT the shortest path)

• Are you thinking of Djikstra's Algorithm en.wikipedia.org/wiki/Dijkstra%27s_algorithm? That does not pass through every point but does find the shortest path.. in implementation a path passing through all points is considered but discarded for being longer than a more direct path, so the same logic applies but a path only becomes valid if it passes through each point once then compare the lenghts of the valid paths and retain the shortest. – Michael Stimson Feb 12 at 7:10
• No, every point should be hit once. Although this is also very interesting, thanks! – Philipp Feb 12 at 7:12
• If you started with a Delaunay triangulation mathworld.wolfram.com/DelaunayTriangulation.html you could extract the edges and look at this as as a shortest path delivery problem, see en.wikipedia.org/wiki/Shortest_path_problem which lists methods (Djikstra's among them). Conceptually the edges would be the roads and points delivery locations, so none can be skipped, a shortest path is sought to minimize the travel for the driver. – Michael Stimson Feb 12 at 7:19
• This is traveling salesperson problem. Going to nearest first usually works. – FelixIP Feb 12 at 8:58