They are typically attracted by the shelter and the worms, and not
what is put on the compost, so pretty well the only effective ways
are turning the heap over and poison.

According to the ratcatcher (Rodent Disposal Operative) from my local
Council rats are very keen on apple and pear skins so when dealing with an
infestation in my compost heap he requested these be disposed of elsewhere.
He also recommended ceasing putting nuts and seeds out for the birds. Brown
rats (Rattus norvigicus) are natural omnivores where a preference for seeds
or grains. One of the main reasons for their success is their adaptability
to live off what foods are available. The much rarer black rat (rattus
rattus) is also an omnivore but tends to eat more vegetable matter. Rats
often carry the spirochete responsible for Weils Disease a.k.a leptospirosis
that is a serious, and indeed potentially fatal condition that is excreted
in the urine.

The bottom line is that rats pose a serious threat to human health and this
is why many councils will provide eradication services free of charge.