The theory of evolution strategies
The theory of evolution strategies
Noisy Local Optimization with Evolution Strategies
Noisy Local Optimization with Evolution Strategies
Where Elitists Start Limping Evolution Strategies at Ridge Functions
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
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
On the use of evolution strategies for optimising certain positive definite quadratic forms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Step length adaptation on ridge functions
Evolutionary Computation
Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge
Natural Computing: an international journal
Exploring the bias of direct search and evolutionary optimization
Exploring the bias of direct search and evolutionary optimization
Optimal weighted recombination
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
On the analysis of self-adaptive evolution strategies on elliptic model: first results
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Theoretical Computer Science
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Cigar functions are convex quadratic functions that are characterised by the presence of only two distinct eigenvalues of their Hessian, the smaller one of which occurs with multiplicity one. Their ridge-like topology makes them a useful test case for optimisation strategies. This paper extends previous work on modelling the behaviour of evolution strategies with isotropically distributed mutations optimising cigar functions by considering weighted recombination as well as the effects of noise on optimisation performance. It is found that the same weights that have previously been seen to be optimal for the sphere and parabolic ridge functions are optimal for cigar functions as well. The influence of the presence of noise on optimisation performance depends qualitatively on the trajectory of the search point, which in turn is determined by the strategy's mutation strength as well as its population size and recombination weights. Analytical results are obtained for the case of cumulative step length adaptation.