Probabilistic analysis of algorithms
Probabilistic analysis of algorithms
The theory of evolution strategies
The theory of evolution strategies
Evolution and Optimum Seeking: The Sixth Generation
Evolution and Optimum Seeking: The Sixth Generation
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Fitness Landscapes Based on Sorting and Shortest Paths Problems
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Theoretical Aspects of Evolutionary Algorithms
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Theoretical Computer Science
Convergence in Evolutionary Programs with Self-Adaptation
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
On the performance of (1, λ)-evolution strategies for theridge function class
IEEE Transactions on Evolutionary Computation
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
Probabilistic runtime analysis of (1 +, λ),ES using isotropic mutations
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Convergence phases, variance trajectories, and runtime analysis of continuous EDAs
Proceedings of the 9th annual conference on Genetic and 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
Weighted recombination evolution strategy on a class of PDQF's
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Performance of the (µ/µ, λ)-σSA-ES on a class of PDQFs
IEEE Transactions on Evolutionary Computation
On spectral invariance of randomized hessian and covariance matrix adaptation schemes
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
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We consider the (1+1) Evolution Strategy, a simple evolutionary algorithm for continuous optimization problems, using so-called Gaussian mutations and the 1/5-rule for the adaptation of the mutation strength. Here, the function $f\colon\mathbb{R}^{n}\to\mathbb{R}$ to be minimized is given by a quadratic form f(x)=x⊤Qx, where Q∈ℝn×n is a positive definite diagonal matrix and x denotes the current search point. This is a natural extension of the well-known Sphere-function (Q=I). Thus, very simple unconstrained quadratic programs are investigated, and the question is addressed how Q effects the runtime. For this purpose, quadratic forms$$ f({\mathbf x}) = \xi\cdot\left({x_{1}}^{2}+\dots+{x_{n/2}}^{2}\right)+{x_{n/2+1}}^{2}+\dots+{x_{n}}^{2} $$ with ξ=ω(1), i. e. 1/ξ→0 as n→∞, and ξ=poly(n) are investigated exemplarily. It is proved that the optimization very quickly stabilizes and that, subsequently, the runtime (defined as the number of f-evaluations) to halve the approximation error is Θ(ξn). Though ξn=poly(n), this result actually shows that the evolving search point indeed creeps along the “gentlest descent” of the ellipsoidal fitness landscape.