Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Randomized algorithms
The theory of evolution strategies
The theory of evolution strategies
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
An Analysis Of The Role Of Offspring Population Size In EAs
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Real royal road functions for constant population size
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
Analysis of a simple evolutionary algorithm for minimization in euclidean spaces
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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
Runtime Analysis of the (μ+1) EA on Simple Pseudo-Boolean Functions
Evolutionary Computation
Probabilistic runtime analysis of (1 +, λ),ES using isotropic mutations
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Convergence phases, variance trajectories, and runtime analysis of continuous EDAs
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Population size versus runtime of a simple evolutionary algorithm
Theoretical Computer Science
A Blend of Markov-Chain and Drift Analysis
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Lower Bounds for Evolution Strategies Using VC-Dimension
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
On the choice of the parent population size*
Evolutionary Computation
Why standard particle swarm optimisers elude a theoretical runtime analysis
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
On the impact of the mutation-selection balance on the runtime of evolutionary algorithms
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Convergence rates of SMS-EMOA on continuous bi-objective problem classes
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
How comma selection helps with the escape from local optima
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
On the analysis of the simple genetic algorithm
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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Evolutionary algorithms (EAs) are general, randomized search heuristics applied successfully to optimization problems both in discrete and in continuous search spaces. In recent years, substantial progress has been made in theoretical runtime analysis of EAs, in particular for pseudo-Boolean fitness functions f:(0,1)n → R. Compared to this, little is known about the runtime of simple and, in particular, more complex EAs for continuous functions f: Rn → R.In this paper, a first rigorous runtime analysis of a population-based EA in continuous search spaces is presented. A simple (μ+1) evolution strategy ((μ+1)ES) that uses Gaussian mutations adapted by the 1/5-rule as its search operator is studied on the well-known Sphere functionand the influence of μ and n on its runtime is examined. By generalizing the proof technique of randomized family trees, developed before w.r.t. discrete search spaces, asymptotically upper and lower bounds on the time for the population to make a predefined progress are derived. Furthermore, the utility of the 1/5-rule in population-based evolution strategies is shown. Finally, the behavior of the (μ+1)ES on multimodal functions is discussed.