Theory of evolution strategies - a tutorial
Theoretical aspects of evolutionary computing
Numerical Optimization of Computer Models
Numerical Optimization of Computer Models
Noisy Local Optimization with Evolution Strategies
Noisy Local Optimization with Evolution Strategies
Step-Size Adaption Based on Non-Local Use of Selection Information
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Completely Derandomized Self-Adaptation in Evolution Strategies
Evolutionary Computation
Weighted multirecombination evolution strategies
Theoretical Computer Science - Foundations of genetic algorithms
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
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
Local performance of the (1 + 1)-ES in a noisy environment
IEEE Transactions on Evolutionary Computation
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This work is concerned with a weighted recombination method for Evolution Strategies (ES) on a class of positive definite quadratic forms (PDQF). In particular, the λopt-ES and the λopt-CSA-ES will be analyzed. A characteristic of both strategies is the use of weighted recombination of all offspring within an iteration step. After obtaining equations describing the evolutionary process, the weights and the progress rate for the λopt-ES will be derived. It is shown that the optimal mutation strength (step size) for the λopt-ES yields an asymptotic limit value of 2κ, where κ is an user-chosen rescaling factor. Afterwards the cumulative step-length adaptation (CSA) is analyzed to determine the target mutation strength (the mutation strength the strategy tries to reach by means of adaptation) and the actually attained mutation strength. For both the asymptotic values are obtained at √2κ. To justify the theoretical results, comparisons with simulations are presented.