Genetic algorithms and classifier systems: foundations and future directions
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The Laplacian spectrum of a graph
SIAM Journal on Matrix Analysis and Applications
Adaptation in natural and artificial systems
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Spectra, Euclidean representations and clusterings of hypergraphs
Discrete Mathematics
Random walks and orthogonal functions associated with highly symmetric graphs
Discrete Mathematics
What makes an optimization problem hard?
Complexity
Correlation length, isotropy and meta-stable states
Proceedings of the 16th annual international conference of the Center for Nonlinear Studies on Landscape paradigms in physics and biology : concepts, structures and dynamics: concepts, structures and dynamics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Genetic algorithms as function optimizers
Genetic algorithms as function optimizers
Mutation-crossover isomorphisms and the construction of discriminating functions
Evolutionary Computation
Evolutionary Computation
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
Artificial Life
Principles in the Evolutionary Design of Digital Circuits—Part I
Genetic Programming and Evolvable Machines
Principles in the Evolutionary Design of Digital Circuits—Part II
Genetic Programming and Evolvable Machines
Fitness landscapes and evolvability
Evolutionary Computation
Experiments with Tuneable Fitness Landscapes
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application
Advances in evolutionary computing
Information Characteristics and the Structure of Landscapes
Evolutionary Computation
Crossover Invariant Subsets of the Search Space for Evolutionary Algorithms
Evolutionary Computation
Understanding elementary landscapes
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
Saddles and barrier in landscapes of generalized search operators
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Elementary bit string mutation landscapes
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
A distance between populations for one-point crossover in genetic algorithms
Theoretical Computer Science
Comprehensive and automatic fitness landscape analysis using heuristiclab
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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A new mathematical representation is proposed for the configuration space structure induced by recombination, which we call “P-structure.” It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental “genotypes” the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier decomposition of fitness landscapes into a superposition of “elementary landscapes.” This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination, the elementary landscapes are exactly the p-spin functions (Walsh functions), that is, the same as the elementary landscapes of the string point mutation spaces (i.e., the hypercube). This supports the notion of a strong homomorphism between string mutation and recombination spaces. However, the effective nearest neighbor correlations on these elementary landscapes differ between mutation and recombination and among different recombination operators. On average, the nearest neighbor correlation is higher for one-point recombination than for uniform recombination. For one-point recombination, the correlations are higher for elementary landscapes with fewer interacting sites as well as for sites that have closer linkage, confirming the qualitative predictions of the Schema Theorem. We conclude that the algebraic approach to fitness landscape analysis can be extended to recombination spaces and provides an effective way to analyze the relative hardness of a landscape for a given recombination operator.