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Single- and multi-objective genetic programming: new bounds for weighted order and majority

Authors:

Anh Nguyen,

Tommaso Urli,

Markus WagnerAuthors Info & Claims

FOGA XII '13: Proceedings of the twelfth workshop on Foundations of genetic algorithms XII

Pages 161 - 172

https://doi.org/10.1145/2460239.2460254

Published: 16 January 2013 Publication History

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Abstract

We consolidate the existing computational complexity analysis of genetic programming (GP) by bringing together sound theoretical proofs and empirical analysis. In particular, we address computational complexity issues arising when coupling algorithms using variable length representation, such as GP itself, with different bloat-control techniques. In order to accomplish this, we first introduce several novel upper bounds for two single- and multi-objective GP algorithms on the generalised Weighted ORDER and MAJORITY problems. To obtain these, we employ well-established computational complexity analysis techniques such as fitness-based partitions, and for the first time, additive and multiplicative drift.

The bounds we identify depend on two measures, the maximum tree size and the maximum population size, that arise during the optimization run and that have a key relevance in determining the runtime of the studied GP algorithms. In order to understand the impact of these measures on a typical run, we study their magnitude experimentally, and we discuss the obtained findings.

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Cited By

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Langdon W(2023)Jaws 30Genetic Programming and Evolvable Machines10.1007/s10710-023-09467-x24:2Online publication date: 22-Nov-2023
https://dl.acm.org/doi/10.1007/s10710-023-09467-x
Langdon W(2021)Genetic programming convergenceGenetic Programming and Evolvable Machines10.1007/s10710-021-09405-923:1(71-104)Online publication date: 30-Aug-2021
https://doi.org/10.1007/s10710-021-09405-9
Doerr BKötzing TGregor Lagodzinski JLengler J(2020)The impact of lexicographic parsimony pressure for ORDER/MAJORITY on the run timeTheoretical Computer Science10.1016/j.tcs.2020.01.011Online publication date: Jan-2020
https://doi.org/10.1016/j.tcs.2020.01.011
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Index Terms

Single- and multi-objective genetic programming: new bounds for weighted order and majority
1. Theory of computation
  1. Design and analysis of algorithms

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Information

Published In

FOGA XII '13: Proceedings of the twelfth workshop on Foundations of genetic algorithms XII

January 2013

198 pages

ISBN:9781450319904

DOI:10.1145/2460239

General Chairs:
Frank Neumann
The University of Adelaide, Australia
,
Kenneth De Jong
George Mason University, USA

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 January 2013

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FOGA '13

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SIGEVO

FOGA '13: Foundations of Genetic Algorithms XII

January 16 - 20, 2013

Adelaide, Australia

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Overall Acceptance Rate 72 of 131 submissions, 55%

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Cited By

View all

Langdon W(2023)Jaws 30Genetic Programming and Evolvable Machines10.1007/s10710-023-09467-x24:2Online publication date: 22-Nov-2023
https://dl.acm.org/doi/10.1007/s10710-023-09467-x
Langdon W(2021)Genetic programming convergenceGenetic Programming and Evolvable Machines10.1007/s10710-021-09405-923:1(71-104)Online publication date: 30-Aug-2021
https://doi.org/10.1007/s10710-021-09405-9
Doerr BKötzing TGregor Lagodzinski JLengler J(2020)The impact of lexicographic parsimony pressure for ORDER/MAJORITY on the run timeTheoretical Computer Science10.1016/j.tcs.2020.01.011Online publication date: Jan-2020
https://doi.org/10.1016/j.tcs.2020.01.011
Kötzing TLagodzinski JLengler JMelnichenko A(2019)Destructiveness of lexicographic parsimony pressure and alleviation by a concatenation crossover in genetic programmingTheoretical Computer Science10.1016/j.tcs.2019.11.036Online publication date: Dec-2019
https://doi.org/10.1016/j.tcs.2019.11.036
Kötzing TLagodzinski JLengler JMelnichenko A(2018)Destructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic ProgrammingParallel Problem Solving from Nature – PPSN XV10.1007/978-3-319-99259-4_4(42-54)Online publication date: 21-Aug-2018
https://doi.org/10.1007/978-3-319-99259-4_4
Doerr BKötzing TLagodzinski JLengler JBosman P(2017)Bounding bloat in genetic programmingProceedings of the Genetic and Evolutionary Computation Conference10.1145/3071178.3071271(921-928)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1145/3071178.3071271
Shi JQian CYu Y(2017)Evolutionary multi-objective optimization made faster by sequential decomposition2017 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2017.7969607(2488-2493)Online publication date: Jun-2017
https://doi.org/10.1109/CEC.2017.7969607
Wagner MNeumann FUrli T(2015)On the performance of different genetic programming approaches for the sorting problemEvolutionary Computation10.1162/EVCO_a_0014923:4(583-609)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1162/EVCO_a_00149
Wagner MNeumann F(2014)Single- and multi-objective genetic programming: New runtime results for sorting2014 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2014.6900310(125-132)Online publication date: Jul-2014
https://doi.org/10.1109/CEC.2014.6900310

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