Randomized algorithms
A computational view of population genetics
Random Structures & Algorithms
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
On the Optimization of Monotone Polynomials by Simple Randomized Search Heuristics
Combinatorics, Probability and Computing
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
The Cooperative Coevolutionary (1+1) EA
Evolutionary Computation
On the Choice of the Offspring Population Size in Evolutionary Algorithms
Evolutionary Computation
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Theory of Computing Systems
Rigorous hitting times for binary mutations
Evolutionary Computation
Real royal road functions for constant population size
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
Theoretical analysis of diversity mechanisms for global exploration
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Population size versus runtime of a simple evolutionary algorithm
Theoretical Computer Science
Convergence Analysis of Evolution Strategies with Random Numbers of Offspring
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
On the choice of the parent population size*
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
On the impact of the mutation-selection balance on the runtime of evolutionary algorithms
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Comparison of simple diversity mechanisms on plateau functions
Theoretical Computer Science
The impact of parametrization in memetic evolutionary algorithms
Theoretical Computer Science
Maximal age in randomized search heuristics with aging
Proceedings of the 11th 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
Insight knowledge in search based software testing
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Comparing Different Aging Operators
ICARIS '09 Proceedings of the 8th International Conference on Artificial Immune Systems
Analysis of diversity-preserving mechanisms for global exploration*
Evolutionary Computation
Theoretical analysis of rank-based mutation: combining exploration and exploitation
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
The benefit of migration in parallel evolutionary algorithms
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Black-box search by unbiased variation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Quasirandom evolutionary algorithms
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Theoretical results in genetic programming: the next ten years?
Genetic Programming and Evolvable Machines
Practical performance models of algorithms in evolutionary program induction and other domains
Artificial Intelligence
Optimal fixed and adaptive mutation rates for the leadingones problem
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
On benefits and drawbacks of aging strategies for randomized search heuristics
Theoretical Computer Science
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Analysis of (1+1) evolutionary algorithm and randomized local search with memory
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 can provably be useful in evolutionary computation
Theoretical Computer Science
The use of tail inequalities on the probable computational time of randomized search heuristics
Theoretical Computer Science
Crossover speeds up building-block assembly
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Computing longest common subsequences with the B-cell algorithm
ICARIS'12 Proceedings of the 11th international conference on Artificial Immune Systems
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
How the (1+λ) evolutionary algorithm optimizes linear functions
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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Although Evolutionary Algorithms (EAs) have been successfully applied to optimization in discrete search spaces, theoretical developments remain weak, in particular for population-based EAs. This paper presents a first rigorous analysis of the (μ+1) EA on pseudo-Boolean functions. Using three well-known example functions from the analysis of the (1+1) EA, we derive bounds on the expected runtime and success probability. For two of these functions, upper and lower bounds on the expected runtime are tight, and on all three functions, the (μ+1) EA is never more efficient than the (1+1) EA. Moreover, all lower bounds grow with μ. On a more complicated function, however, a small increase of μ provably decreases the expected runtime drastically.This paper develops a new proof technique that bounds the runtime of the (μ+1) EA. It investigates the stochastic process for creating family trees of individuals; the depth of these trees is bounded. Thereby, the progress of the population towards the optimum is captured. This new technique is general enough to be applied to other population-based EAs.