Drift analysis and average time complexity of evolutionary algorithms
Artificial Intelligence
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
A study of drift analysis for estimating computation time of evolutionary algorithms
Natural Computing: an international journal
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
A Blend of Markov-Chain and Drift Analysis
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Computing single source shortest paths using single-objective fitness
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
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
Runtime analysis of the (1+1) evolutionary algorithm on strings over finite alphabets
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Theory of Randomized Search Heuristics: Foundations and Recent Developments
When do evolutionary algorithms optimize separable functions in parallel?
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
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We analyze the run-time of the (1 + 1) Evolutionary Algorithm optimizing an arbitrary linear function f : {0,1,...,r}n - R. If the mutation probability of the algorithm is p = c/n, then (1 + o(1))(ec/c))rn log n + O(r3n log log n) is an upper bound for the expected time needed to find the optimum. We also give a lower bound of (1 + o(1))(1/c)rn log n. Hence for constant c and all r slightly smaller than (log n)1/3, our bounds deviate by only a constant factor, which is e(1 + o(1)) for the standard mutation probability of 1/n. The proof of the upper bound uses multiplicative adaptive drift analysis as developed in a series of recent papers. We cannot close the gap for larger values of r, but find indications that multiplicative drift is not the optimal analysis tool for this case.