Evolution and Optimum Seeking: The Sixth Generation
Evolution and Optimum Seeking: The Sixth Generation
Noisy Local Optimization with Evolution Strategies
Noisy Local Optimization with Evolution Strategies
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
On the Choice of the Offspring Population Size in Evolutionary Algorithms
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 simple evolutionary algorithm for minimization in euclidean spaces
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Rigorous analyses of simple diversity mechanisms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Examining the Effect of Elitism in Cellular Genetic Algorithms Using Two Neighborhood Structures
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
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We investigate (1,λ) ESs using isotropic mutations for optimization in ℝn by means of a theoretical runtime analysis. In particular, a constant offspring-population size λ will be of interest. We start off by considering an adaptation-less (1,2) ES minimizing a linear function. Subsequently, a piecewise linear function with a jump/cliff is considered, where a (1+λ) ES gets trapped, i.e., (at least) an exponential (in n) number of steps are necessary to escape the local-optimum region. The (1,2) ES, however, manages to overcome the cliff in an almost unnoticeable number of steps. Finally, we outline (because of the page limit) how the reasoning and the calculations can be extended to the scenario where a (1,λ) ES using Gaussian mutations minimizes Cliff, a bimodal, spherically symmetric function already considered in the literature, which is merely Sphere with a jump in the function value at a certain distance from the minimum. For λ a constant large enough, the (1,λ) ES manages to conquer the global-optimum region – in contrast to (1+λ) ESs which get trapped.