Conditions for Implicit Parallelism

Many interesting varieties of genetic algorithms have been designed and implemented in the last fifteen years. One way to improve our understanding of genetic algorithms is to identify properties that are invariant across these seemingly different versions. This paper focuses on invariants among genetic algorithms that differ along two dimensions: (1) the way user-defined objective function is mapped to a fitness measure, and (2) the way the fitness measure is used to assign offspring to parents. A genetic algorithm is called admissible if it meets what seem to be the weakest reasonable requirements along these dimensions. It is shown that any admissible genetic algorithm exhibits a form of implicit parallelism.