Are there any cryptocoin protocols that permanently remove the processing power advantage in mining in a mathematically verifiable way, so that specialized equipment can never be developed to game the algorithms?   Perhaps a genetic algo that evolves?

Thwarting botnets and other parallel processing attacks seems difficult if you rely on processors to do the work.  What about requiring a human to participate in the work?  Maybe image recognition work that computers currently can't do like solving capchas?