Graph algorithms and NP-completeness
Graph algorithms and NP-completeness
Multiple-Way Network Partitioning
IEEE Transactions on Computers
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
Genetic Algorithms and Grouping Problems
Genetic Algorithms and Grouping Problems
Group properties of crossover and mutation
Evolutionary Computation
Spin-flip symmetry and synchronization
Evolutionary Computation
A New Genetic Local Search Algorithm for Graph Coloring
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
A Grouping Genetic Algorithm for Graph Colouring and Exam Timetabling
PATAT '00 Selected papers from the Third International Conference on Practice and Theory of Automated Timetabling III
Redundant representations in evolutionary computation
Evolutionary Computation
New topologies for genetic search space
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Geometric crossover for multiway graph partitioning
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Representations for Genetic and Evolutionary Algorithms
Representations for Genetic and Evolutionary Algorithms
Geometric crossovers for multiway graph partitioning
Evolutionary Computation
Feasibility-preserving crossover for maximum k-coverage problem
Proceedings of the 10th annual conference on Genetic and evolutionary computation
A graph matching method and a graph matching distance based on subgraph assignments
Pattern Recognition Letters
On the locality of representations
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
Normalization in genetic algorithms
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Representation invariant genetic operators
Evolutionary Computation
Properties of Symmetric Fitness Functions
IEEE Transactions on Evolutionary Computation
Normalization for Genetic Algorithms With Nonsynonymously Redundant Encodings
IEEE Transactions on Evolutionary Computation
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We extend a geometric framework for the interpretation of search operators to encompass the genotype-phenotype mapping derived from an equivalence relation defined by an isometry group. We show that this mapping can be naturally interpreted using the concept of quotient space, in which the original space corresponds to the genotype space and the quotient space corresponds to the phenotype space. Using this characterization, it is possible to define induced geometric crossovers on the phenotype space (called quotient geometric crossovers). These crossovers have very appealing properties for non-synonymously redundant encodings, such as reducing the size of the search space actually searched, removing the low locality from the encodings, and allowing a more informed search by utilizing distances better tailored to the specific solution interpretation. Interestingly, quotient geometric crossovers act on genotypes but have an effect equivalent to geometric crossovers acting directly on the phenotype space. This property allows us to actually implement them even when phenotypes cannot be represented directly. We give four example applications of quotient geometric crossovers for non-synonymously redundant encodings and demonstrate their superiority experimentally.