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Fixed Budget Performance of the (1+1) EA on Linear Functions

Published: 17 January 2015 Publication History

Abstract

We present a fixed budget analysis of the (1+1) evolutionary algorithm for general linear functions, considering both the quality of the solution after a predetermined 'budget' of fitness function evaluations (a priori) and the improvement in quality when the algorithm is given additional budget, given the quality of the current solution (a posteriori). Two methods are presented: one based on drift analysis, the other on the differential equation method and Chebyshev's inequality. While the first method is superior for general linear functions, the second can be more precise for specific functions and provides concentration guarantees. As an example, we provide tight a posteriori fixed budget results for the function OneMax.

References

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  • (2024)Can Evolutionary Clustering Have Theoretical Guarantees?IEEE Transactions on Evolutionary Computation10.1109/TEVC.2023.329664528:5(1220-1234)Online publication date: Oct-2024
  • (2024)Tight Runtime Bounds for Static Unary Unbiased Evolutionary Algorithms on Linear FunctionsAlgorithmica10.1007/s00453-024-01258-986:10(3115-3152)Online publication date: 22-Jul-2024
  • (2023)Tight Runtime Bounds for Static Unary Unbiased Evolutionary Algorithms on Linear FunctionsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590482(1565-1574)Online publication date: 15-Jul-2023
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    cover image ACM Conferences
    FOGA '15: Proceedings of the 2015 ACM Conference on Foundations of Genetic Algorithms XIII
    January 2015
    200 pages
    ISBN:9781450334341
    DOI:10.1145/2725494
    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 the author(s) 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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    Publication History

    Published: 17 January 2015

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    Author Tags

    1. (1+1) ea
    2. evolutionary algorithm
    3. fixed budget
    4. linear functions
    5. theory

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    FOGA '15
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    FOGA '15: Foundations of Genetic Algorithms XIII
    January 17 - 22, 2015
    Aberystwyth, United Kingdom

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    FOGA '15 Paper Acceptance Rate 16 of 26 submissions, 62%;
    Overall Acceptance Rate 72 of 131 submissions, 55%

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    Cited By

    View all
    • (2024)Can Evolutionary Clustering Have Theoretical Guarantees?IEEE Transactions on Evolutionary Computation10.1109/TEVC.2023.329664528:5(1220-1234)Online publication date: Oct-2024
    • (2024)Tight Runtime Bounds for Static Unary Unbiased Evolutionary Algorithms on Linear FunctionsAlgorithmica10.1007/s00453-024-01258-986:10(3115-3152)Online publication date: 22-Jul-2024
    • (2023)Tight Runtime Bounds for Static Unary Unbiased Evolutionary Algorithms on Linear FunctionsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590482(1565-1574)Online publication date: 15-Jul-2023
    • (2023)Runtime Analysis with Variable CostProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590432(1611-1618)Online publication date: 15-Jul-2023
    • (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
    • (2021)On the impact of the performance metric on efficient algorithm configurationArtificial Intelligence10.1016/j.artint.2021.103629(103629)Online publication date: Nov-2021
    • (2021)Fixed-Target Runtime AnalysisAlgorithmica10.1007/s00453-021-00881-084:6(1762-1793)Online publication date: 3-Nov-2021
    • (2021)MATE: A Model-Based Algorithm Tuning EngineEvolutionary Computation in Combinatorial Optimization10.1007/978-3-030-72904-2_4(51-67)Online publication date: 27-Mar-2021
    • (2020)Fixed-target runtime analysisProceedings of the 2020 Genetic and Evolutionary Computation Conference10.1145/3377930.3390184(1295-1303)Online publication date: 25-Jun-2020
    • (2020)Improved Fixed-Budget Results via Drift AnalysisParallel Problem Solving from Nature – PPSN XVI10.1007/978-3-030-58115-2_45(648-660)Online publication date: 2-Sep-2020
    • Show More Cited By

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