Some Theoretical Properties of Evolutionary Algorithms under Partially Ordered Fitness Values

Abstract

Presently, the limit theory of evolutionary algorithms (EA) for mono-criterion optimization under certainty is well developed. The situation is different for the fields of evolutionary optimization under complete or partial uncertainty, multiple criteria and so forth. Since these problem classes may be seen as special cases of the task of finding the set of minimal (or maximal) elements in partially ordered sets, a limit theory for EAs that can cope with this kind of problem passes all properties and results on its special cases mentioned above.