On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Comparing global and local mutations on bit strings
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Is "best-so-far" a good algorithmic performance metric?
Proceedings of the 10th annual conference on Genetic and evolutionary computation
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
Drift analysis with tail bounds
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation
Algorithmica - Special Issue: Theory of Evolutionary Computation
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Sharp bounds by probability-generating functions and variable drift
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Fixed budget computations: a different perspective on run time analysis
Proceedings of the 14th annual conference on Genetic and evolutionary computation
The choice of the offspring population size in the (1,λ) EA
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Analyzing Evolutionary Algorithms: The Computer Science Perspective
Analyzing Evolutionary Algorithms: The Computer Science Perspective
Artificial immune systems for optimisation
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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At last year's GECCO a novel perspective for theoretical performance analysis of evolutionary algorithms and other randomised search heuristics was introduced that concentrates on the expected function value after a pre-defined number of steps, called budget. This is significantly different from the common perspective where the expected optimisation time is analysed. While there is a huge body of work and a large collection of tools for the analysis of the expected optimisation time the new fixed budget perspective introduces new analytical challenges. Here it is shown how results on the expected optimisation time that are strengthened by deviation bounds can be systematically turned into fixed budget results. We demonstrate our approach by considering the (1+1) EA on LeadingOnes and significantly improving previous results. We prove that deviating from the expected time by an additive term of ω(n3/2 happens only with probability o(1). This is turned into tight bounds on the function value using the inverse function. We use three, increasingly strong or general approaches to proving the deviation bounds, namely via Chebyshev's inequality, via Chernoff bounds for geometric random variables, and via variable drift analysis.