Randomized algorithms
Theory of evolutionary algorithms: a bird's eye view
Theoretical Computer Science - Special issue on evolutionary computation
Theoretical Computer Science
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
Towards an analytic framework for analysing the computation time of evolutionary algorithms
Artificial Intelligence
On the benefits of populations for noisy optimization
Evolutionary Computation
Real royal road functions for constant population size
Theoretical Computer Science
On the Optimization of Monotone Polynomials by Simple Randomized Search Heuristics
Combinatorics, Probability and Computing
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
Real royal road functions: where crossover provably is essential
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
The Cooperative Coevolutionary (1+1) EA
Evolutionary Computation
On the Choice of the Offspring Population Size in Evolutionary Algorithms
Evolutionary Computation
Runtime Analysis of the (μ+1) EA on Simple Pseudo-Boolean Functions
Evolutionary Computation
Probabilistic runtime analysis of (1 +, λ),ES using isotropic mutations
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Theory of Computing Systems
Rigorous hitting times for binary mutations
Evolutionary Computation
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
The analysis of a recombinative hill-climber on H-IFF
IEEE Transactions on Evolutionary Computation
On the utility of the population size for inversely fitness proportional mutation rates
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
On the impact of the mutation-selection balance on the runtime of evolutionary algorithms
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Benefits of a population: five mechanisms that advantage population-based algorithms
IEEE Transactions on Evolutionary Computation
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Runtime analysis of the (1+1) EA on computing unique input output sequences
Information Sciences: an International Journal
| Hi-index | 5.23 |
Evolutionary algorithms (EAs) find numerous applications, and practical knowledge on EAs is immense. In practice, sophisticated population-based EAs employing selection, mutation and crossover are applied. In contrast, theoretical analysis of EAs often concentrates on very simple algorithms such as the (1+1) EA, where the population size equals 1. In this paper, the question is addressed whether the use of a population by itself can be advantageous. A population-based EA that neither makes use of crossover nor any diversity-maintaining operator is investigated on an example function. It is shown that an increase of the population size by a constant factor decreases the expected runtime from exponential to polynomial. Thereby, the best gap known so far is improved from superpolynomial vs. polynomial to exponential vs. polynomial. Moreover, it is proved that the exponential and polynomial runtime bounds occur with a probability exponentially close to one if the population size is a constant (resp., a small polynomial). Finally, a second example function, where only a small population leads to a polynomial runtime, and a hierarchy result on the appropriate population size are presented. The analyses show formally how the population size can lead to different attractors in the search space.