Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
A building-block royal road where crossover is provably essential
Proceedings of the 9th 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
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
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
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
Crossover speeds up building-block assembly
Proceedings of the 14th annual conference on Genetic and evolutionary computation
On the analysis of the simple genetic algorithm
Proceedings of the 14th annual conference on Genetic and evolutionary computation
The choice of the offspring population size in the (1,λ) EA
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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A runtime analysis of the Simple Genetic Algorithm (SGA) for the OneMax problem has recently been presented proving that the algorithm requires exponential time with overwhelming probability. This paper presents an improved analysis which overcomes some limitations of our previous one. Firstly, the new result holds for population sizes up to mu = n1/4-epsilon which is an improvement up to a power of 2 larger. Secondly, we present a technique to bound the diversity of the population that does not require a bound on its bandwidth. Apart from allowing a stronger result, we believe this is a major improvement towards the reusability of the techniques in future systematic analyses of GAs. Finally, we consider the more natural SGA using selection with replacement rather than without replacement although the results hold for both algorithmic versions. Experiments are presented to explore the limits of the new and previous mathematical techniques.