On classifications of fitness functions
Theoretical aspects of evolutionary computing
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
Schemata, Distributions and Graphical Models in Evolutionary Optimization
Journal of Heuristics
From Recombination of Genes to the Estimation of Distributions I. Binary Parameters
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Modern Heuristic Optimization Techniques With Applications To Power Systems
Modern Heuristic Optimization Techniques With Applications To Power Systems
Drift and Scaling in Estimation of Distribution Algorithms
Evolutionary Computation
Space Complexity of Estimation of Distribution Algorithms
Evolutionary Computation
A comparison of selection schemes used in evolutionary algorithms
Evolutionary Computation
Fda -a scalable evolutionary algorithm for the optimization of additively decomposed functions
Evolutionary Computation
An application of a multivariate estimation of distribution algorithm to cancer chemotherapy
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Analyzing probabilistic models in hierarchical BOA
IEEE Transactions on Evolutionary Computation - Special issue on evolutionary algorithms based on probabilistic models
Analysis of computational time of simple estimation of distribution algorithms
IEEE Transactions on Evolutionary Computation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Using previous models to bias structural learning in the hierarchical boa
Evolutionary Computation
A comparison of predictive measures of problem difficulty inevolutionary algorithms
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
On the convergence of a class of estimation of distribution algorithms
IEEE Transactions on Evolutionary Computation
Protein Folding in Simplified Models With Estimation of Distribution Algorithms
IEEE Transactions on Evolutionary Computation
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Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms EDAs. By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space .