How do i get rid of rats in my backyard?

so, there's a bunch of rats in my backyard. there's lots of trees and leafy growth back there. the yard is huge and slopes down to a busy street. really, there's very little yard and mostly woods back there. so we can only reasonably take care of about 1/3 or less of the area. my roommates and i are afraid that they will eventually try to get into our house (there was one on our porch today). the people upstairs from us like to compost and they have a bin in the backyard. this seems to be attracting a lot of the rats. shy of asking them to stop composting, (a request i doubt they will be receptive to) is there any other ways to eradicate or curb this rat problem? thank you in advance.