Bus stops problem

[acertijo4ever]

Hi all, I have the following problem I need to solve, and I hope you can point me to the right direction.

 

I have a bunch (4000) of people addresses in a city that are mapped to coordinates (longitude and latitude). I also have different bus routes (up to 17), that go through the city picking up these people, that I could draw to google maps for example. This routes were designed based on human experience, and the buses that travel on them practically have to stop every time a person raises one's hand (sometimes on every block), which is pretty inefficient.

 

What I would like to do is to define a number of Bus Stops, along all of the routes, that comply with the following restrictions:

- Each bus stop groups the most people near that point according to their addresses.

- The number of Bus Stops doesn't have to be the minimun available, but the best in order for people not to walk too far from their houses.

- The routes should not be modified.

 

I know there's a lot of work to be done so I'd appreciate any help.

 

Regards.

Joel