What is the clearest way to display multiple routes on a map that are overlapping eachother?

Question

I'm in need of some HCI advice.

Here is what my current implementation of a 'best path between multiple required vertices' looks like:

Black is the start vertex, green is the end vertex, and blue are the 'inbetween' vertices that must be visited.

I have added an alpha of 70% to different coloured paths, obviously that hasn't helped distinguish the different routes between each vertex.

What would be the optimal way to display these routes at the same time, so that someone can distinguish the route from 1 to 2, and 3 to the last vertex?