What are the algorithms for finding the optimal path?

Question

Mathematics

Please tell me if there are algorithms for finding the optimal route, if both arcs (paths) and vertices (points) have weight. For example, there are 10 points on the map, points will be awarded for visiting each point, the number of points depends on the specific point. I heard about Dijkstra's algorithms, Warshall, I heard about the transport problem, but I can't understand what to do if not only arcs but also vertices have weight?!

Answer 1

It doesn't seem to really matter much when it comes to Dijkstra's algorithm. It is enough when passing the next edge, in addition to adding its weight, also add the weight of its paired vertex (after all, an edge always connects 2 vertices).
And what kind of task, where it is required to take into account both the weights of the edges and the weights of the vertices? Some kind of educational or generated by the real world? :)

Answer 2

Ant algorithm