research-article

Runtime Analysis for the Parameter-less Population Pyramid

Authors:

Brian W. Goldman,

Dirk SudholtAuthors Info & Claims

GECCO '16: Proceedings of the Genetic and Evolutionary Computation Conference 2016

Pages 669 - 676

https://doi.org/10.1145/2908812.2908846

Published: 20 July 2016 Publication History

Abstract

Runtime analysis of black-box search algorithms provides rigorous performance guarantees, aiding in algorithm design and comparison. Unfortunately, deriving bounds can be challenging and as a result existing literature has focused on simplistic algorithms. The Parameter-less Population Pyramid (P3) is a recently proposed (Goldman and Punch, GECCO 2014) unbiased black-box search algorithm that combines local search, model based mixing, and population layering. In empirical studies P3 has outperformed leading genetic algorithms across a variety of problems.

We provide a runtime analysis on n-bit problems to help shed light on the reason for P3's effectiveness. We derive upper runtime bounds of n+1 for linear functions, {n²+1} for LeadingOnes, and O(2^k n log(n/k)) for Concatenated Traps of size k. For a simplified version of P3 we obtain a bound of O(n log³ n) for H-IFF. These results show P3 is competitive with the best known unbiased genetic algorithms on each of these problems, suggesting its performance generalizes well. Furthermore, we find that P3's effectiveness relies on all three of its major components, lending support to the algorithm's design.

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Cited By

Przewozniczek MKomarnicki M(2021)Fitness Caching - From a Minor Mechanism to Major Consequences in Modern Evolutionary Computation2021 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC45853.2021.9504686(1785-1791)Online publication date: 28-Jun-2021
https://doi.org/10.1109/CEC45853.2021.9504686
Foster MHughes MO'Brien GOliveto PPyle JSudholt DWilliams JCoello Coello C(2020)Do sophisticated evolutionary algorithms perform better than simple ones?Proceedings of the 2020 Genetic and Evolutionary Computation Conference10.1145/3377930.3389830(184-192)Online publication date: 25-Jun-2020
https://dl.acm.org/doi/10.1145/3377930.3389830
Lehre PSudholt D(2020)Parallel Black-Box Complexity With Tail BoundsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2019.295423424:6(1010-1024)Online publication date: Dec-2020
https://doi.org/10.1109/TEVC.2019.2954234
Show More Cited By

Index Terms

Runtime Analysis for the Parameter-less Population Pyramid
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Discrete optimization
        Optimization with randomized search heuristics
2. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes

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cover image ACM Conferences

GECCO '16: Proceedings of the Genetic and Evolutionary Computation Conference 2016

July 2016

1196 pages

ISBN:9781450342063

DOI:10.1145/2908812

Editor:
Tobias Friedrich
Hasso Plattner Institute
,
General Chair:
Frank Neumann
University of Adelaide
,
Program Chair:
Andrew M. Sutton
Hasso Plattner Institute

Copyright © 2016 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: 20 July 2016

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European Union Seventh Framework Programme (FP7/2007-2013)

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GECCO '16

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SIGEVO

GECCO '16: Genetic and Evolutionary Computation Conference

July 20 - 24, 2016

Colorado, Denver, USA

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GECCO '16 Paper Acceptance Rate 137 of 381 submissions, 36%;

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

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Cited By

Przewozniczek MKomarnicki M(2021)Fitness Caching - From a Minor Mechanism to Major Consequences in Modern Evolutionary Computation2021 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC45853.2021.9504686(1785-1791)Online publication date: 28-Jun-2021
https://doi.org/10.1109/CEC45853.2021.9504686
Foster MHughes MO'Brien GOliveto PPyle JSudholt DWilliams JCoello Coello C(2020)Do sophisticated evolutionary algorithms perform better than simple ones?Proceedings of the 2020 Genetic and Evolutionary Computation Conference10.1145/3377930.3389830(184-192)Online publication date: 25-Jun-2020
https://dl.acm.org/doi/10.1145/3377930.3389830
Lehre PSudholt D(2020)Parallel Black-Box Complexity With Tail BoundsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2019.295423424:6(1010-1024)Online publication date: Dec-2020
https://doi.org/10.1109/TEVC.2019.2954234
Doerr CAuger AStützle T(2019)Dynamic parameter choices in evolutionary computationProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3319619.3323372(890-922)Online publication date: 13-Jul-2019
https://dl.acm.org/doi/10.1145/3319619.3323372
Doerr CTakadama K(2018)Dynamic parameter choices in evolutionary computationProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3205651.3207851(800-830)Online publication date: 6-Jul-2018
https://dl.acm.org/doi/10.1145/3205651.3207851
Gandomi AGoldman B(2018)Parameter-less population pyramid for large-scale tower optimizationExpert Systems with Applications: An International Journal10.1016/j.eswa.2017.11.04796:C(175-184)Online publication date: 15-Apr-2018
https://dl.acm.org/doi/10.1016/j.eswa.2017.11.047
Doerr C(2017)Non-static parameter choices in evolutionary computationProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3067695.3067707(736-761)Online publication date: 15-Jul-2017
https://dl.acm.org/doi/10.1145/3067695.3067707

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