Probabilistic analysis of evolution strategies using isotropic mutations [Elektronische Ressource] / von Jens Jägersküpper

DoachbAnalysisDoofvonEvolutionderStrategiesamUsingInfoJ?gersk?ppMutations2006DissertationUniversit?tzurrtmundErlangungFdesGradesrmatikeinesJensDoktoerrsrtmundderTag der mündlichen Prüfung: 19. Dezember 2006Dekan: Professor Dr. Peter BuchholzGutachter: Professor Dr. Ingo Wegener,Juniorprofessor Dr. Thomas JansennThis dissertation deals with optimization in high-dimensional Euclidean spaceR . Namely, aparticular type of direct-search methods known as Evolution Strategies (ESs) are investigated.Evolution Strategies mimic natural evolution, in particular mutation, in order to “evolve” an ap-proximate solution.As this dissertation focuses on theoretical investigation of ESs in the way randomized approx-imation algorithms are analyzed in theoretical computer science (rather than by means of conver-gence theory or dynamical-system theory), very basic and simple ESs are considered. Namely,the only search operator that is applied are so-called isotropic mutations. That is, a new candidatesolution is obtained by adding a random vector to the current candidate solution the distributionof which is spherically symmetric.General lower bounds on the number of steps/isotropic mutations which are necessary to reducethe approximation error in the search space are proved, where the focus is on how the number ofoptimization steps depends on (and scales with) the dimensionality of the search space.