Geometric Crossovers for Real-coded Genetic Algorithms (under review)



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 general setting and show that many pre-existing genetic operators for 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 and design a boundary extension method on this glued space for making the fitness function smooth at the boundary. We compare their performance with existing crossovers on test functions which are commonly used in the literature.


IEEE transactions on evolutionary computation, October 2008

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