Convergence results for the (1, λ)-SA-ES using the theory of ϕ-irreducible Markov chains
Theoretical Computer Science
Completely Derandomized Self-Adaptation in Evolution Strategies
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
Exponential natural evolution strategies
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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The information geometric optimization (IGO) flow has been introduced recently by Arnold et al. This distinguished mathematical flow on the parameter manifold of a family of search distributions constitutes a novel approach to the analysis of several randomized search heuristics, including modern evolution strategies. Besides its appealing theoretical properties, it offers the unique opportunity to approach the convergence analysis of evolution strategies in two independent steps. The first step is the analysis of the flow itself, or more precisely, the convergence of its trajectories to Dirac peaks over the optimum. In a second step it remains to study the deviation of actual algorithm trajectories from the continuous flow. The present study approaches the first problem. The IGO flow of isotropic Gaussian search distributions is analyzed on convex, quadratic fitness functions. Convergence of all trajectories to the Dirac peak over the optimum is established.