Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
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
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Theoretical Computer Science
Aiming for a theoretically tractable CSA variant by means of empirical investigations
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Precision, local search and unimodal functions
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Oblivious Randomized Direct Search for Real-Parameter Optimization
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Convergence Analysis of Evolution Strategies with Random Numbers of Offspring
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
A Blend of Markov-Chain and Drift Analysis
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Why standard particle swarm optimisers elude a theoretical runtime analysis
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Tight lower bounds for greedy routing in uniform small world rings
Proceedings of the forty-first annual ACM symposium on Theory of computing
Brief announcement: tight lower bounds for greedy routing in uniform small world rings
Proceedings of the 28th ACM symposium on Principles of distributed computing
A self-stabilizing algorithm for cut problems in synchronous networks
Theoretical Computer Science
Analysis of particle interaction in particle swarm optimization
Theoretical Computer Science
Empirical investigation of simplified step-size control in metaheuristics with a view to theory
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Theoretical analysis of evolutionary computation on continuously differentiable functions
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Quasirandom evolutionary algorithms
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Convergence rates of (1+1) evolutionary multiobjective optimization algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Tight bounds for blind search on the integers and the reals
Combinatorics, Probability and Computing
Free lunches on the discrete Lipschitz class
Theoretical Computer Science
Convergence rates of SMS-EMOA on continuous bi-objective problem classes
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Information Sciences: an International Journal
Sharp bounds by probability-generating functions and variable drift
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Information Sciences: an International Journal
Lower bounds for randomized direct search with isotropic sampling
Operations Research Letters
Analysis of a natural gradient algorithm on monotonic convex-quadratic-composite functions
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Lower bounds for hit-and-run direct search
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
A median success rule for non-elitist evolution strategies: study of feasibility
Proceedings of the 15th annual conference on Genetic and evolutionary computation
How the (1+λ) evolutionary algorithm optimizes linear functions
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Hi-index | 5.24 |
In practical optimization, applying evolutionary algorithms has nearly become a matter of course. Their theoretical analysis, however, is far behind practice. So far, theorems on the runtime are limited to discrete search spaces; results for continuous search spaces are limited to convergence theory or even rely on validation by experiments, which is unsatisfactory from a theoretical point of view. The simplest, or most basic, evolutionary algorithms use a population consisting of only one individual and use random mutations as the only search operator. Here the so-called (1+1) evolution strategy for minimization in R^n is investigated when it uses isotropically distributed mutation vectors. In particular, so-called Gaussian mutations are analyzed when the so-called 1/5-rule is used for their adaptation. Obviously, a reasonable analysis must respect the function to be minimized, and furthermore, the runtime must be measured with respect to the approximation error. A first algorithmic analysis of how the runtime depends on n, the dimension of the search space, is presented. This analysis covers all unimodal functions that are monotone with respect to the distance from the optimum. It turns out that, in the scenario considered, Gaussian mutations in combination with the 1/5-rule indeed ensure asymptotically optimal runtime; namely, @Q(n) steps/function evaluations are necessary and sufficient to halve the approximation error.