On a hand-built multiclass benchmark, (1+1)-ENAS with one-bit or bit-wise mutation finds an optimal architecture in O(rM ln(rM)) expected generations, with lower bound Omega(rM ln M), so the two mutations have nearly equal runtime.
Comparing global and local mutations on bit strings
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Runtime Analysis of Evolutionary NAS for Multiclass Classification
On a hand-built multiclass benchmark, (1+1)-ENAS with one-bit or bit-wise mutation finds an optimal architecture in O(rM ln(rM)) expected generations, with lower bound Omega(rM ln M), so the two mutations have nearly equal runtime.