Structure evolution and incomplete induction

Abstract

Evolutionary strategies such as the evolution strategy (Rechenberg 1965, 1973; Schwefel 1977) or genetic algorithms (Holland 1975; Goldberg 1989) have been widely applied to systems where parameters have to be determined according to a particular objective function. A necessary demand in all these experiments is that the structures of the objects to be optimised are well defined, because these structures are part of the objective function. With structure evolution the range of applications of evolutionary algorithms can now be expanded to tasks which are less accurately described, i.e. where the structures of the objects are fairly unknown. Heuristical effort is reduced first to defining structure components by combinations of which the structure space is generated. The structure space can be nearly infinitely large. Furthermore, the mutation procedures for structures have to be determined, complying with the demand for strong causality. In its computer model the algorithm of structure evolution involves the phenomenon of isolation, a feature of biological evolution additional to replication, mutation, and selection, which have already been implemented in other strategies. The idea of structure evolution is to let different but some what similar structures of an object compete in temporarily isolated populations where the respective parameter evolution is carried out. Thus structure evolution can perform a most effective search, both in structure and parameter space. The algorithm is demonstrated with two examples: a neural filter in a visual system and the topologies of frameworks. The first of the examples touches the problem of incompletely described tasks, and this paper will show that the effect of “overlearning” can be avoided by a learning procedure called “incomplete induction”, which fits best with the algorithm of structure evolution.