I've been breeding rats for about a year now, at first I was separating the females when they had babies, but now I actually keep the male and female and babies all in the same tub, I'm using an ARS rat breeding rack. I've never once had a problem with rats eating their babies, although I've had mice do it on occasion, and only when they have their first litter and don't realize what the babies are. The problem with separating the males is that you have to wait for the babies to be weaned, then put the male and female together again at which point there is varying degrees of fighting, then you have to wait another month for the female to get pregnant and have babies. If you keep the male and female together the females will have more babies as soon as the first batch is weaned, it doubles your production. You can actually have half as many male / female tubs than when you separate the females.
I also keep my mice in breeding colonies of one male to 3-5 females. I had a few problems with cannibalism at first in one tank but it doesn't last long once the moms raise up a batch or two of babies. When my mice and rats are at weanling stage I separate them into male / female tubs to keep them from getting pregnant and fighting. And I thin out the numbers as they get older so I don't overcrowded the tubs. Right now I'm experiencing some tail chewing in some of my rat tubs, I've never seen that before, maybe just too many rats per tub. I fed off the few babies with chewed tails first and started putting more food blocks right in the tubs instead of just overhead in the feeders, I think that will help.