On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
On the Choice of the Mutation Probability for the (1+1) EA
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
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
Crossover is provably essential for the Ising model on trees
GECCO '05 Proceedings of the 7th annual conference on Genetic and 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
The one-dimensional Ising model: mutation versus recombination
Theoretical Computer Science
A building-block royal road where crossover is provably essential
Proceedings of the 9th 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
General lower bounds for the running time of evolutionary algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
General scheme for analyzing running times of parallel evolutionary algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Analysis of evolutionary algorithms: from computational complexity analysis to algorithm engineering
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
How crossover helps in pseudo-boolean optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Running time analysis of Ant Colony Optimization for shortest path problems
Journal of Discrete Algorithms
Crossover can provably be useful in evolutionary computation
Theoretical Computer Science
The analysis of a recombinative hill-climber on H-IFF
IEEE Transactions on Evolutionary Computation
When do evolutionary algorithms optimize separable functions in parallel?
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
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
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We re-investigate a fundamental question: how effective is crossover in combining building blocks? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter we prove that a simple GA with uniform crossover is twice as fast as the fastest EA using only standard bit mutation, up to small-order terms. The reason is that crossover effectively turns neutral mutations into improvements by combining the right building blocks at a later stage. Compared to mutation-based EAs, this makes multi-bit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from 1/n to (1+5)/2 Å 1/n H 1.618/n. Similar results are proved for k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building-block functions.