SIAM Review
Topological crossover for the permutation representation
GECCO '05 Proceedings of the 7th annual workshop on Genetic and evolutionary computation
Geometric crossover for multiway graph partitioning
Proceedings of the 8th annual conference on Genetic and evolutionary computation
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Geometric crossover for sets, multisets and partitions
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Geometric crossover for biological sequences
EuroGP'06 Proceedings of the 9th European conference on Genetic Programming
Evolutionary computation: comments on the history and current state
IEEE Transactions on Evolutionary Computation
Effects of the use of non-geometric binary crossover on evolutionary multiobjective optimization
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Diversity improvement by non-geometric binary crossover in evolutionary multiobjective optimization
IEEE Transactions on Evolutionary Computation
Geometric nelder-mead algorithm on the space of genetic programs
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Geometry of evolutionary algorithms
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Geometric differential evolution on the space of genetic programs
EuroGP'10 Proceedings of the 13th European conference on Genetic Programming
Geometry of evolutionary algorithms
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Geometric differential evolution for combinatorial and programs spaces
Evolutionary Computation
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Geometric crossover is a representation-independent generalization of traditional crossover for binary strings. It is defined in a simple geometric way by using the distance associated with the search space. Many interesting recombination operators for the most frequently used representations are geometric crossovers under some suitable distance. Showing that a given recombination operator is a geometric crossover requires finding a distance for which offspring are in the metric segment between parents. However, proving that a recombination operator is not a geometric crossover requires excluding that one such distance exists. It is, therefore, very difficult to draw a clear-cut line between geometric crossovers and non-geometric crossovers. In this paper we develop some theoretical tools to solve this problem and we prove that some well-known operators are not geometric. Finally, we discuss the implications of these results.