Randomized algorithms
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
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Evolutionary Computation
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
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 Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming)
On the analysis of the (1+1) memetic algorithm
Proceedings of the 8th annual conference on Genetic and evolutionary computation
On the effect of populations in evolutionary multi-objective optimization
Proceedings of the 8th annual conference on Genetic and evolutionary computation
On the impact of objective function transformations on evolutionary and black-box algorithms
Genetic Programming and Evolvable Machines
Rigorous analyses of simple diversity mechanisms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Finding large cliques in sparse semi-random graphs by simple randomized search heuristics
Theoretical Computer Science
How mutation and selection solve long-path problems in polynomial expected time
Evolutionary Computation
IEEE Transactions on Evolutionary Computation
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Lessons from the black-box: fast crossover-based genetic algorithms
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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Evolutionary algorithms (EAs) are population-based randomized search heuristics that often solve problems successfully. Here the focus is on the possible effects of changing the parent population size in a simple, but still realistic, mutation-based EA. It preserves diversity by avoiding duplicates in its population. On the one hand its behavior on well-known pseudo-Boolean example functions is investigated by means of a rigorous runtime analysis. A comparison with the expected runtime of the algorithm's variant that does not avoid duplicates demonstrates the strengths and weaknesses of maintaining diversity. On the other hand, newly developed functions are presented for which the optimizer considered that even a decrease of the population size by a single increment leads from efficient optimization to enormous runtime and overwhelming probability. This is proven for all feasible population sizes and thereby this result forms a hierarchy theorem. In order to obtain all these results new methods for the analysis of the EA are developed.