The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
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
A building-block royal road where crossover is provably essential
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Crossover can provably be useful in evolutionary computation
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Rigorous analyses of fitness-proportional selection for optimizing linear functions
Proceedings of the 10th annual conference on Genetic and 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
Theoretical analysis of fitness-proportional selection: landscapes and efficiency
Proceedings of the 11th 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
A few ants are enough: ACO with iteration-best update
Proceedings of the 12th annual conference on Genetic and evolutionary computation
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation
Algorithmica - Special Issue: Theory of Evolutionary Computation
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Theory of Randomized Search Heuristics: Foundations and Recent Developments
How crossover helps in pseudo-boolean optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
On the effectiveness of crossover for migration in parallel evolutionary algorithms
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Fitness-levels for non-elitist populations
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Sharp bounds by probability-generating functions and variable drift
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Convergence analysis of canonical genetic algorithms
IEEE Transactions on Neural Networks
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Lessons from the black-box: fast crossover-based genetic algorithms
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Improved runtime analysis of the simple genetic algorithm
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
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For many years it has been a challenge to analyze the time complexity of Genetic Algorithms (GAs) using stochastic selection together with crossover and mutation. This paper presents a rigorous runtime analysis of the well-known Simple Genetic Algorithm (SGA) for OneMax. It is proved that the SGA has exponential runtime with overwhelming probability for population sizes up to μ≤ n1/8-ε for some arbitrarily small constant ε and problem size n. To the best of our knowledge, this is the first time non-trivial lower bounds are obtained on the runtime of a standard crossover-based GA for a standard benchmark function. The presented techniques might serve as a first basis towards systematic runtime analyses of GAs.