Geometric Unification of Evolutionary Algorithms

Evolutionary algorithms are only superficially different and can be unified within an axiomatic geometric framework by abstraction of the solution representation. This framework describes the evolutionary search in a representation-independent way, purely in geometric terms, paving the road to a general theory of evolutionary algorithms. It also leads to a principled design methodology for the crossover operator for any solution representation. 1 Context of the research Evolutionary Algorithms (EAs) are successful and widespread general problem solving methods that mimic in a simplified manner biological evolution. Whereas all EAs share the same basic algorithmic structure, they differ in the solution representation the genotype and in the search operators employed mutation and crossover that are representation-specific. Is this difference only superficial? Is there a deeper unity encompassing all mutation and crossover operators beyond the specific representation, hence all EAs? So far, no one has been able to attack this question successfully and has proposed a general mathematical framework that unifies search operators for all solution representations. In the research community there is a strong feeling that the EC field needs unification and systematization in a rational framework to survive its own exceptional growth (De Jong [4]). Beside De Jong, there are important researchers who have been promoting EC unification: Radcliffe pioneered a unified theory of representations [11], although he never used the word “unification”. Riccardo Poli unified the schema theorem for traditional genetic algorithms and genetic programming [3]. Chris Stephens suggests that all evolutionary algorithms can be unified using the language of dynamical systems and coarse graining [1]. Franz Rothlauf has initiated a theory of representations [12]. 2 Research and study 2.1 Research questions and goals My research questions are: