The theory of evolution strategies
The theory of evolution strategies
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Convergence in Evolutionary Programs with Self-Adaptation
Evolutionary Computation
Self-adaptive mutations may lead to premature convergence
IEEE Transactions on Evolutionary Computation
Rigorous runtime analysis of a (μ+1)ES for the sphere function
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Probabilistic runtime analysis of (1 +, λ),ES using isotropic mutations
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Analysis of a multiobjective evolutionary algorithm on the 0-1 knapsack problem
Theoretical Computer Science
How the (1 + 1) ES using isotropic mutations minimizes positive definite quadratic forms
Theoretical Computer Science - Foundations of genetic algorithms
On the use of evolution strategies for optimising certain positive definite quadratic forms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Aiming for a theoretically tractable CSA variant by means of empirical investigations
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Step length adaptation on ridge functions
Evolutionary Computation
Evolutionary tuning of multiple SVM parameters
Neurocomputing
Empirical investigation of simplified step-size control in metaheuristics with a view to theory
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
How comma selection helps with the escape from local optima
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Running time analysis of a multiobjective evolutionary algorithm on simple and hard problems
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Rigorous runtime analysis of the (1+1) ES: 1/5-rule and ellipsoidal fitness landscapes
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Lower bounds for hit-and-run direct search
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
Convergence of the IGO-Flow of isotropic gaussian distributions on convex quadratic problems
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
International Journal of Metaheuristics
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Although evolutionary algorithms (EAs) are widely used in practical optimization, their theoretical analysis is still in its infancy. Up to now results on the (expected) runtime are limited to discrete search spaces, yet EAs are mostly applied to continuous optimization problems. So far results on the runtime of EAs for continuous search spaces rely on validation by experiments/simulations since merely a simplifying model of the respective stochastic process is investigated. Here a first algorithmic analysis of the expected runtime of a simple, but fundamental EA for the search space Rn is presented. Namely, the so-called (1+1) Evolution Strategy ((1+1) ES) is investigated on unimodal functions that are monotone with respect to the distance between search point and optimum. A lower bound on the expected run-time is proven under the only assumption that isotropic distributions are used to generate the random mutation vectors. Consequently, this bound holds for any mutation adaptation mechanism. Finally, we prove that the commonly used "Gauss mutations" in combination with the so-called 1/5-rule for the mutation adaptation do achieve asymptotically optimalexp ected runtime.