Randomized algorithms
On evolutionary exploration and exploitation
Fundamenta Informaticae
Evolutionary Optimization
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Calculating the expected loss of diversity of selection schemes
Evolutionary Computation
Proceedings of the 3rd International Conference on Genetic Algorithms
A study of drift analysis for estimating computation time of evolutionary algorithms
Natural Computing: an international journal
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
Runtime Analysis of the (μ+1) EA on Simple Pseudo-Boolean Functions
Evolutionary Computation
Predictive models for the breeder genetic algorithm i. continuous parameter optimization
Evolutionary Computation
A comparison of selection schemes used in evolutionary algorithms
Evolutionary Computation
Rigorous analyses of fitness-proportional selection for optimizing linear functions
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Population size versus runtime of a simple evolutionary algorithm
Theoretical Computer Science
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Using markov-chain mixing time estimates for the analysis of ant colony optimization
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Non-uniform mutation rates for problems with unknown solution lengths
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Non-existence of linear universal drift functions
Theoretical Computer Science
Runtime analysis of the (1+1) EA on computing unique input output sequences
Information Sciences: an International Journal
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The interplay between the mutation operator and the selection mechanism plays a fundamental role in the behaviour of evolutionary algorithms. However, this interplay is still not completely understood. This paper presents a rigorous runtime analysis of a non-elitistic population based evolutionary algorithm that uses the linear ranking selection mechanism. The analysis focuses on how the balance between parameter η controlling the selection pressure in linear ranking selection, and parameter χ controlling the bit-wise mutation rate impacts the expected runtime. The results point out situations where a correct balance between selection pressure and mutation rate is essential for finding the optimal solution in polynomial time. In particular, it is shown that there exist fitness functions which under a certain assumption can be solved in polynomial time if the ratio between parameters η and χ is appropriately tuned to the problem instance class, but where a small change in this ratio can increase the runtime exponentially. Furthermore, it is shown that the appropriate parameter choice depends on the characteristics of the fitness function. Hence there does in general not exists a problem-independent optimal balance between mutation rate and selection pressure. The results are obtained using new techniques based on branching processes.