Probabilistic analysis of algorithms
Probabilistic analysis of algorithms
The theory of evolution strategies
The theory of evolution strategies
Evolution and Optimum Seeking: The Sixth Generation
Evolution and Optimum Seeking: The Sixth Generation
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Theoretical Computer Science
Convergence in Evolutionary Programs with Self-Adaptation
Evolutionary Computation
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
On the use of evolution strategies for optimising certain positive definite quadratic forms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Proceedings of the 10th 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
Weighted recombination evolution strategy on a class of PDQF's
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Why standard particle swarm optimisers elude a theoretical runtime analysis
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Neuroevolution strategies for episodic reinforcement learning
Journal of Algorithms
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
Convergence rates of (1+1) evolutionary multiobjective optimization algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
On the behaviour of evolution strategies optimising cigar functions
Evolutionary Computation
Convergence rates of SMS-EMOA on continuous bi-objective problem classes
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Information Sciences: an International Journal
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
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The (1+1) evolution strategy (ES), a simple, mutation-based evolutionary algorithm for continuous optimization problems, is analyzed. In particular, we consider the most common type of mutations, namely Gaussian mutations, and the 1/5-rule for mutation adaptation, and we are interested in how the runtime/number of function evaluations to obtain a predefined reduction of the approximation error depends on the dimension of the search space.The most discussed function in the area of ES is the so-called SPHERE-function given by SPHERE: Rn → R with x↦x⊤Ix (where I ∈ Rn×n is the identity matrix), which also has already been the subject of a runtime analysis. This analysis is extended to arbitrary positive definite quadratic forms that induce ellipsoidal fitness landscapes which are "close to being spherically symmetric", showing that the order of the runtime does not change compared to SPHERE. Furthermore, certain positive definite quadratic forms fRn → R with x↦x⊤Qx, where Q ∈ Rn×n, inducing ellipsoidal fitness landscapes that are "far away from being spherically symmetric" are exemplarily investigated, namely f(x)=ξċ(x12 +...+ xn/22)+xn/2+12 +...+ xn2 with ξ= poly(n) such that 1/ξ → 0 as n → ∞. It is proved that the optimization very quickly stabilizes and that, subsequently, the runtime to halve the approximation error is Θ(ξ ċ n) compared to Θ(n) for SPHERE.