Drift analysis and average time complexity of evolutionary algorithms
Artificial Intelligence
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
On the Choice of the Mutation Probability for the (1+1) EA
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
PPSN III Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: Parallel Problem Solving from Nature
Setting The Mutation Rate: Scope And Limitations Of The 1/L Heuristic
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
A Blend of Markov-Chain and Drift Analysis
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Limitations of existing mutation rate heuristics and how a rank GA overcomes them
IEEE Transactions on Evolutionary Computation
On the brittleness of evolutionary algorithms
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Quasirandom evolutionary 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
Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation
Algorithmica - Special Issue: Theory of Evolutionary Computation
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Non-uniform mutation rates for problems with unknown solution lengths
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Mutation rates of the (1+1)-EA on pseudo-boolean functions of bounded epistasis
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Evolutionary algorithms for the project scheduling problem: runtime analysis and improved design
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Mutation rate matters even when optimizing monotonic functions
Evolutionary Computation
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Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these functions are easy to optimize. The choice of the constant c in the mutation probability p(n) = c/n can make a decisive difference. We show that if c 1, then the (1+1) EA finds the optimum of every such function in Θ(n log n) iterations. For c = 1, we can still prove an upper bound of O(n3/2). However, for c 33, we present a strictly monotone function such that the (1+1) EA with overwhelming probability does not find the optimum within 2Ω(n) iterations. This is the first time that we observe that a constant factor change of the mutation probability changes the run-time by more than constant factors.