The theory of evolution strategies
The theory of evolution strategies
Numerical Optimization of Computer Models
Numerical Optimization of Computer Models
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Probabilistic runtime analysis of (1 +, λ),ES using isotropic mutations
Proceedings of the 8th annual conference on Genetic and evolutionary computation
How the (1 + 1) ES using isotropic mutations minimizes positive definite quadratic forms
Theoretical Computer Science - Foundations of genetic algorithms
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
Theoretical Computer Science
Analysis of a simple evolutionary algorithm for minimization in euclidean spaces
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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Randomized direct-search methods for the optimization of a function f : Rn → R given by a black box for f-evaluations are investigated. We consider the cumulative step-size adaptation (CSA) for the variance of multivariate zero-mean normal distributions. Those are commonly used to sample new candidate solutions within metaheuristics, in particular within the CMA Evolution Strategy (CMA-ES), a state-of-the-art direct-search method. Though the CMA-ES is very successful in practical optimization, its theoretical foundations are very limited because of the complex stochastic process it induces. To forward the theory on this successful method, we propose two simplifications of the CSA used within CMA-ES for step-size control. We show by experimental and statistical evaluation that they perform sufficiently similarly to the original CSA (in the considered scenario), so that a further theoretical analysis is in fact reasonable. Furthermore, we outline in detail a probabilistic/theoretical runtime analysis for one of the two CSA-derivatives.