Surprisingly you can solve massive TSPs using heuristics. The solutions are not guaranteed to be optimal, but they can get very close to optimal without a crazy amount of computing power.
The Concorde TSP solver can apparently solve instances with 85.6k cities to optimality. Pretty amazing!
Sorry but how is ride share problem a TSP problem? Rides are assigned one at a time and I do not think they would take into account future rides while doing the assignment optimization.
Not my industry, but imagining that they accept rides within a 48 hour windows from now. You’d quickly get something somewhat similar to a TSP. But given that you have lots of additional constraints (people tend to have a clear idea when they want to get from A to B) compared to the classical TSP, it might actually be easier to solve. As those constraints limit the paths you must evaluate.
The Concorde TSP solver can apparently solve instances with 85.6k cities to optimality. Pretty amazing!