When I had mice the solution was sealing every tiny hole to the outside. Mice can come through a hole about 1/2″ in diameter. The exterminator filled all holes and cracks with steel wool and/or that expandable foam stuff. After he did so, we killed the ones already in the house with snap traps, and that was that. I assume rats are the same, only ickier.
Also, it’s probably not a bad idea to stick a poison bait station outside. I have one, and I refill the poison about once a month.