research-article

A method to derive fixed budget results from expected optimisation times

Authors:

Benjamin Doerr,

Christine ZargesAuthors Info & Claims

GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation

Pages 1581 - 1588

https://doi.org/10.1145/2463372.2463565

Published: 06 July 2013 Publication History

Abstract

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(n^3/2 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.

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Cited By

Doerr BLi XHandl J(2024)A Gentle Introduction to Theory (for Non-Theoreticians)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3648402(800-829)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3648402
Doerr BKnowles JNeumann ANeumann FLi XHandl J(2024)A Block-Coordinate Descent EMO Algorithm: Theoretical and Empirical AnalysisProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654169(493-501)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654169
Doerr BKelley A(2024)Fourier Analysis Meets Runtime Analysis: Precise Runtimes on PlateausAlgorithmica10.1007/s00453-024-01232-586:8(2479-2518)Online publication date: 10-May-2024
https://doi.org/10.1007/s00453-024-01232-5
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Index Terms

A method to derive fixed budget results from expected optimisation times
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation

July 2013

1672 pages

ISBN:9781450319638

DOI:10.1145/2463372

Editor:
Christian Blum
IKERBASQUE and University of the Basque Country UPV/EHU, Spain
,
General Chair:
Enrique Alba
University of Malaga, Spain

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 July 2013

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GECCO '13

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SIGEVO

GECCO '13: Genetic and Evolutionary Computation Conference

July 6 - 10, 2013

Amsterdam, The Netherlands

Acceptance Rates

GECCO '13 Paper Acceptance Rate 204 of 570 submissions, 36%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

Doerr BLi XHandl J(2024)A Gentle Introduction to Theory (for Non-Theoreticians)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3648402(800-829)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3648402
Doerr BKnowles JNeumann ANeumann FLi XHandl J(2024)A Block-Coordinate Descent EMO Algorithm: Theoretical and Empirical AnalysisProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654169(493-501)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654169
Doerr BKelley A(2024)Fourier Analysis Meets Runtime Analysis: Precise Runtimes on PlateausAlgorithmica10.1007/s00453-024-01232-586:8(2479-2518)Online publication date: 10-May-2024
https://doi.org/10.1007/s00453-024-01232-5
Doerr BSilva SPaquete L(2023)A Gentle Introduction to Theory (for Non-Theoreticians)Proceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3595042(946-975)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583133.3595042
Bossek JSudholt D(2023)Do Additional Target Points Speed Up Evolutionary Algorithms?Theoretical Computer Science10.1016/j.tcs.2023.113757(113757)Online publication date: Feb-2023
https://doi.org/10.1016/j.tcs.2023.113757
Wang CHe JChen YZou X(2022)Influence of Binomial Crossover on Approximation Error of Evolutionary AlgorithmsMathematics10.3390/math1016285010:16(2850)Online publication date: 10-Aug-2022
https://doi.org/10.3390/math10162850
Doerr BWagner M(2022)A gentle introduction to theory (for non-theoreticians)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3520304.3533628(890-921)Online publication date: 9-Jul-2022
https://dl.acm.org/doi/10.1145/3520304.3533628
Vinokurov DBuzdalov MWagner M(2022)On optimal static and dynamic parameter choices for fixed-target optimizationProceedings of the Genetic and Evolutionary Computation Conference10.1145/3512290.3528875(876-883)Online publication date: 8-Jul-2022
https://dl.acm.org/doi/10.1145/3512290.3528875
Doerr BKötzing T(2022)Lower Bounds from Fitness Levels Made EasyAlgorithmica10.1007/s00453-022-00952-w86:2(367-395)Online publication date: 28-Apr-2022
https://doi.org/10.1007/s00453-022-00952-w
Vinokurov DBuzdalov M(2022)Towards Fixed-Target Black-Box Complexity AnalysisParallel Problem Solving from Nature – PPSN XVII10.1007/978-3-031-14721-0_42(600-611)Online publication date: 15-Aug-2022
https://doi.org/10.1007/978-3-031-14721-0_42
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