Drift analysis and average time complexity of evolutionary algorithms
Artificial Intelligence
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Towards an analytic framework for analysing the computation time of evolutionary algorithms
Artificial Intelligence
On the effect of populations in evolutionary multi-objective optimization
Proceedings of the 8th annual conference on Genetic and evolutionary computation
How mutation and selection solve long-path problems in polynomial expected time
Evolutionary Computation
The gambler's ruin problem, genetic algorithms, and the sizing of populations
Evolutionary Computation
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
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
Theoretical analysis of fitness-proportional selection: landscapes and efficiency
Proceedings of the 11th Annual conference on Genetic and 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
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Drift analysis with tail bounds
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
Fitness-levels for non-elitist populations
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Non-existence of linear universal drift functions
Theoretical Computer Science
On the analysis of the simple genetic algorithm
Proceedings of the 14th 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
Population size matters: rigorous runtime results for maximizing the hypervolume indicator
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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Rigorous runtime analyses of evolutionary algorithms (EAs) mainly investigate algorithms that use elitist selection methods. Two algorithms commonly studied are Randomized Local Search (RLS) and the (1+1) EA and it is well known that both optimize any linear pseudo-Boolean function on n bits within an expected number of O(n log n) fitness evaluations. In this paper, we analyze variants of these algorithms that use fitness proportional selection. A well-known method in analyzing the local changes in the solutions of RLS is a reduction to the gambler's ruin problem. We extend this method in order to analyze the global changes imposed by the (1+1) EA. By applying this new technique we show that with high probability using fitness proportional selection leads to an exponential optimization time for any linear pseudo-Boolean function with non-zero weights. Even worse, all solutions of the algorithms during an exponential number of fitness evaluations differ with high probability in linearly many bits from the optimal solution. Our theoretical studies are complemented by experimental investigations which confirm the asymptotic results on realistic input sizes.