Design und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence On the Complexity of Overcoming Gaps When Using Elitist Selection and Isotropic Mutations
نویسنده
چکیده
We consider the (1+λ) evolution strategy, an evolutionary algorithm for minimization in Rn, using isotropic mutations. Thus, for instance, Gaussian mutations adapted by the 1/5-rule or by σ-self-adaptation are covered. Lower bounds on the (expected) runtime (defined as the number of function evaluations) to overcome a gap in the search space are proved (where the search faces a gap of size ∆ if the distance between the current search point and the set of all better points is at least ∆), showing when the runtime is potentially polynomial and when the runtime is necessarily super-polynomial or even necessarily exponential in n, the dimensionality of the search space.
منابع مشابه
Sonderforschungsbereich 531: Design und Management komplexer Prozesse und Systeme mit Methoden der Computational Intelligence
متن کامل
Design und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence Why Comma Selection Can Help with the Escape from Local Optima
We investigate (1,λ) ESs using isotropic mutations for optimization in R 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 le...
متن کاملDesign und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence TAKEOVER TIME IN PARALLEL POPULATIONS WITH MIGRATION
The term takeover time regarding selection methods used in evolutionary algorithms denotes the (expected) number of iterations of the selection method until the entire population consists of copies of the best individual, provided that the initial population consists of a single copy of the best individual whereas the remaining individuals are worse. Here, this notion is extended to parallel su...
متن کاملDesign und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence Pareto Set and EMOA Bahavior for Simple Multimodal Multiobjective Functions
Recent research on evolutionary multiobjective optimization has mainly focused on Pareto-fronts. However, we state that proper behavior of the utilized algorithms in decision/search space is necessary for obtaining good results if multimodal objective functions are concerned. Therefore, it makes sense to observe the development of Pareto-sets as well. We do so on a simple, configurable problem,...
متن کاملDesign und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence Pareto Set and EMOA Behavior for Simple Multimodal Multiobjective Functions
Recent research on evolutionary multiobjective optimization has mainly focused on Pareto-fronts. However, we state that proper behavior of the utilized algorithms in decision/search space is necessary for obtaining good results if multimodal objective functions are concerned. Therefore, it makes sense to observe the development of Pareto-sets as well. We do so on a simple, configurable problem,...
متن کامل