I am the Chairman of the Democratic Party in my county. In preparing for an upcoming election, I need to post a notice on the door of 21 voting sites. All 21 are within my county and are rural addresses. Is there a site or app I can use to enter all 21 addresses and have the app/site map out the shortest possible route that hits all 21 (well, 22 locations including home, where I will start and end) locations?
Thanks.
There are a lot of commercial applications for this kind of thing:
but your best bet for a small circuit, one-time routing over real-life roads is probably to mark the sites on a paper road map and figure it out for yourself.
There’s http://findthebestroute.com/ and https://www.speedyroute.com/
Edit: SpeedyRoute is easier to use.
Specifically, it’s the Traveling Salesman Problem, which is known to be one of the hardest problems in computation. With 23 stops, you’re not going to get the optimum solution, even with every computer in the world working on it. You can, however, get a good-enough solution.
This is pretty irrelevant to the OP’s actual real-world problem, but I think it’s more accurate to say that with 23 stops, it’s possible that he’s not going to be able to find the optimum solution or know that he has it , even with more computing power than exists in the world.
He may get the optimum solution just by luck the first thing he tries (though without being able to prove there’s no better one). And of course, the actual possible connections between the stops might be degenerate enough that it is completely solvable in practical time.
Does it have to calculate 23! (factorial) routes?
Hi, we run the optimal route planner www.speedyroute.com mentioned by a poster earlier in the thread.
For the curious, there are several optimisations that can be performed so that an optimal route can be obtained without calculating every possible route.
Speedy Route for example calculates the routes between each location and its immediate neighbours, using Google Directions to obtain realistic travel times and distances. These results are then collated to provide a ‘grid’ of possible routes from each location to the next. It isn’t necessary to calculate a direct route between e.g. a location on the far west of your route and another on the far east, as any route you take will pass through the intermediate locations anyway.
Finally the grid of routes is fed into a Travelling Salesman Calculator (Speedy Route uses the excellent OptaPlanner see www.optaplanner.org) to calculate the optimal route between all the locations.
Hope this helps understand the process a little more!
I’ll bet you’re really an R but wanted to increase your chances of getting some help here. (That’s what I’d do!) 
Ha! That’s funny. No, I’m really the Democratic County chair. Go me!