finding an optimized path

hello out there,

im having problems to achieve the following.

i have a surface with points on it. startpoint, endpoint and attractor points.
a line should be drawn on the surface by maintaing the following rules.

go through startpoint and endpoint, and pass also the attractorpoint (or strive for it) but move so that in the end its the shortest way.
i think the solution is something like a gradient descent, but at with a target.

maybe someone can give me a hint ?
help is appreciated very much - thank you