It is best for laying hens and broilers to have feed available 24/7. Use a good treadle feeder with a counterweight and spring loaded door, installed correctly and train the bird using the instructions and not common sense. Chicken feed does attract rats and mice but only if you use the wrong feeder.
A good feeder will have a lip on front that projects back into the feed bin and that will stop 95% of the birds that rake feed. For the other 5%, get a feed lip extension to solve the raking. Avoid mixed grain feed as birds will try to rake the feed to get to the tasty bits, or just use a good feeder. Do a forum search for treadle feeders and you will run across our feeder and a review by Howard E. that is very good. Howard E. also wrote one heck of a post on getting rid of rats, best I have ever seen. But the first step is sanitation and that means a proper treadle feeder with a spring loaded door and a counterweight. All the other treadle feeders can be pushed open by rats.