The theory of evolution strategies
The theory of evolution strategies
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Numerical Optimization of Computer Models
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Evolutionary Computation
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IEEE Transactions on Evolutionary Computation
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Evo'08 Proceedings of the 2008 conference on Applications of evolutionary computing
Conditioning, halting criteria and choosing λ
EA'07 Proceedings of the Evolution artificielle, 8th international conference on Artificial evolution
Log-linear convergence and optimal bounds for the (1 + 1)-ES
EA'07 Proceedings of the Evolution artificielle, 8th international conference on Artificial evolution
Mirrored sampling and sequential selection for evolution strategies
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
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Applied Soft Computing
Mirrored sampling in evolution strategies with weighted recombination
Proceedings of the 13th annual conference on Genetic and evolutionary computation
On the behaviour of the (1, λ)-es for a conically constrained problem
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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This paper investigates the limits of the predictions based on the classical progress rate theory for Evolution Strategies. We explain on the sphere function why positive progress rates give convergence in mean, negative progress rates divergence in mean and show that almost sure convergence can take place despite divergence in mean. Hence step-sizes associated to negative progress can actually lead to almost sure convergence. Based on these results we provide an alternative progress rate definition related to almost sure convergence. We present Monte Carlo simulations to investigate the discrepancy between both progress rates and therefore both types of convergence. This discrepancy vanishes when dimension increases. The observation is supported by an asymptotic estimation of the new progress rate definition.