Finite Markov chain results in evolutionary computation: a tour d'horizon
Fundamenta Informaticae
Drift analysis and average time complexity of evolutionary algorithms
Artificial Intelligence
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
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
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
Theoretical Computer Science
Optimizing monotone functions can be difficult
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Runtime analysis of the (1+1) evolutionary algorithm on strings over finite alphabets
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Simple max-min ant systems and the optimization of linear pseudo-boolean functions
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Tight analysis of the (1+1)-ea for the single source shortest path problem
Evolutionary Computation
Revisiting the restricted growth function genetic algorithm for grouping problems
Evolutionary Computation
Non-existence of linear universal drift functions
Theoretical Computer Science
Proceedings of the 14th annual conference on Genetic and evolutionary computation
A bisimulation-based method of concept learning for knowledge bases in description logics
Proceedings of the Third Symposium on Information and Communication Technology
On algorithm-dependent boundary case identification for problem classes
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
When do evolutionary algorithms optimize separable functions in parallel?
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
How the (1+λ) evolutionary algorithm optimizes linear functions
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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In their seminal article [Theo. Comp. Sci. 276(2002):51---82] Droste, Jansen, and Wegener present the first theoretical analysis of the expected runtime of a basic direct-search heuristic with a global search operator, namely the (1+1) Evolutionary Algorithm (EA), for the class of linear functions over the search space {0,1}n. In a rather long and involved proof they show that, for any linear function, the expected runtime of the EA is O(nlogn), i.e., that there are two constants cand n茂戮驴 such that, for n茂戮驴 n茂戮驴, the expected number of iterations until a global optimum is generated is bound above by c·nlogn. However, neither cnor n茂戮驴 are specified --- they would be pretty large. Here we reconsider this optimization scenario to demonstrate the potential of an analytical method that makes use not only of the drift (w.r.t. a potential function, here the number of bits set correctly), but also of the distribution of the evolving candidate solution over the search space {0,1}n: An invariance property of this distribution is proved, which is then used to derive a significantly better lower bound on the drift. Finally, this better estimate of the drift results in an upper bound on the expected number of iterations of 3.8 nlog2n+ 7.6log2nfor n茂戮驴 2.