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
Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization
Proceedings of the 5th International Conference on Genetic Algorithms
Muiltiobjective optimization using nondominated sorting in genetic algorithms
Evolutionary Computation
Foundations of Global Genetic Optimization
Foundations of Global Genetic Optimization
An EMO algorithm using the hypervolume measure as selection criterion
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
Multiobjective evolutionary strategy for finding neighbourhoods of pareto-optimal solutions
EvoApplications'13 Proceedings of the 16th European conference on Applications of Evolutionary Computation
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In the paper we consider the ranking given by the Pareto dominance relation as a basis to create a selection operator for the Evolutionary Multiobjective Optimization Algorithm (EMOA). Assuming that sampling to the next epoch is performed according to the generalized Bernoulli schema with regard to a selected type of the rank selection, a heuristic operator for EMOA is introduced. Having defined the heuristic operator, the transition probability matrix of the uniform Markov chain modeling EMOA can be explicitly obtained as in the Vose's theory of the Simple Genetic Algorithm (SGA). This chain is ergodic if the mixing operator following the EMOA selection operator in each epoch is strictly positive. Moreover, we show that the measure on the space of populations imposed by the EMOA infinite population concentrates on the set of fixed points of the heuristic operator after infinite number of epochs, assuming that the heuristic operator is focusing.