CSM-466: Geometric Crossovers for Real-code Representation

Geometric crossover is a representation-independent generalization of the class of traditional mask-based crossover for binary strings. It is based on the distance of the search space seen as a metric space. Although real-code representation allows for a very familiar notion of distance, namely the Euclidean distance, there are also other distances suiting it. Also, topological transformations of the real space give rise to further notions of distance. In this paper, we study the geometric crossovers associated with these distances in a formal and very general setting and show that many preexisting genetic operators for the real-code representation are geometric crossovers. We also propose a novel methodology to remove the inherent bias of pre-existing geometric operators by formally transforming topologies to have the same effect as gluing boundaries

Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation. Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space. We give many example applications of the quotient geometric crossover

Geometric Crossovers for Real-code Representation

Geometric crossover is a representation-independent generalization of the class of traditional mask-based crossover for binary strings. It is based on the distance of the search space seen as a metric space. Although real-code representation allows for a very familiar notion of distance, namely the Euclidean distance, there are also other distances suiting it. Also, topological transformations of the real space give rise to further notions of distance. In this paper, we study the geometric crossovers associated with these distances in a formal and very general setting and show that many preexisting genetic operators for the real-code representation are geometric crossovers. We also propose a novel methodology to remove the inherent bias of pre-existing geometric operators by formally transforming topologies to have the same effect as gluing boundaries