research-article

Canonical representation genetic programming

Authors:

John R. Woodward,

Ruibin BaiAuthors Info & Claims

GEC '09: Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation

Pages 585 - 592

https://doi.org/10.1145/1543834.1543914

Published: 12 June 2009 Publication History

Abstract

Search spaces sampled by the process of Genetic Programming often consist of programs which can represent a function in many different ways. Thus, when the space is examined it is highly likely that different programs may be tested which represent the same function, which is an undesirable waste of resources. It is argued that, if a search space can be constructed where only unique representations of a function are permitted, then this will be more successful than employing multiple representations. When the search space consists of canonical representations it is called a canonical search space, and when Genetic Programming is applied to this search space, it is called Canonical Representation Genetic Programming. The challenge lies in constructing these search spaces. With some function sets this is a trivial task, and with some function sets this is impossible to achieve. With other function sets it is not clear how the goal can be achieved. In this paper, we specically examine the search space dened by the function set f+;À; _; =g and the terminal set fx; 1g. Drawing inspiration from the fundamental theorem of arithmetic, and results regarding the fundamental theorem of algebra, we construct a representation where each function that can be constructed with this primitive set has a unique representation. Abbreviations: Genetic Programming (GP), Genetic Algorithm (GA), The No Free Lunch Theorem (NFL) Keywords: canonical representation, standard form, evolutionary computation, genetic programming, no free lunch, bias, symmetric functions, inverse functions, complementary functions, isomorphic representations.

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Cited By

El Krari MGuibadj RWoodward JRobilliard D(2023)Fairer Comparisons for Travelling Salesman Problem Solutions Using Hash FunctionsEvolutionary Computation in Combinatorial Optimization10.1007/978-3-031-30035-6_1(1-15)Online publication date: 31-Mar-2023
https://doi.org/10.1007/978-3-031-30035-6_1
Tauritz DWoodward JAuger AStützle T(2019)Hyper-heuristics tutorialProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3319619.3323382(770-805)Online publication date: 13-Jul-2019
https://dl.acm.org/doi/10.1145/3319619.3323382
Krawiec KSimons CSwan JWoodward J(2018)Metaheuristic Design PatternsHandbook of Research on Emergent Applications of Optimization Algorithms10.4018/978-1-5225-2990-3.ch001(1-36)Online publication date: 2018
https://doi.org/10.4018/978-1-5225-2990-3.ch001
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Canonical representation genetic programming

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Published In

cover image ACM Conferences

GEC '09: Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation

June 2009

1112 pages

ISBN:9781605583266

DOI:10.1145/1543834

General Chairs:
Lihong Xu
Tongji University, China
,
Erik D. Goodman
Michigan State University, USA
,
Program Chairs:
Guoliang Chen
University of Sci. & Tech. of China
,
Darrell Whitley
Colorado State University, USA
,
Yongsheng Ding
Donghua University, China

Copyright © 2009 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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Published: 12 June 2009

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GEC '09

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GEC '09: GEC '09 - ACM/SIGEVO Genetic and Evolutionary Computation Summit

June 12 - 14, 2009

Shanghai, China

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El Krari MGuibadj RWoodward JRobilliard D(2023)Fairer Comparisons for Travelling Salesman Problem Solutions Using Hash FunctionsEvolutionary Computation in Combinatorial Optimization10.1007/978-3-031-30035-6_1(1-15)Online publication date: 31-Mar-2023
https://doi.org/10.1007/978-3-031-30035-6_1
Tauritz DWoodward JAuger AStützle T(2019)Hyper-heuristics tutorialProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3319619.3323382(770-805)Online publication date: 13-Jul-2019
https://dl.acm.org/doi/10.1145/3319619.3323382
Krawiec KSimons CSwan JWoodward J(2018)Metaheuristic Design PatternsHandbook of Research on Emergent Applications of Optimization Algorithms10.4018/978-1-5225-2990-3.ch001(1-36)Online publication date: 2018
https://doi.org/10.4018/978-1-5225-2990-3.ch001
Parque VMiyashita T(2018)Unranking Combinations Using Gradient-Based Optimization2018 IEEE 30th International Conference on Tools with Artificial Intelligence (ICTAI)10.1109/ICTAI.2018.00094(579-586)Online publication date: Nov-2018
https://doi.org/10.1109/ICTAI.2018.00094
Parque VMiyashita T(2018)Towards the Succinct Representation of m Out of nInternet and Distributed Computing Systems10.1007/978-3-030-02738-4_2(16-26)Online publication date: 17-Oct-2018
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Du JWimmer HRada R(2014)Knowledge constrained evolutionary algorithmsInternational Journal of Artificial Intelligence and Soft Computing10.1504/IJAISC.2014.0658014:4(335-353)Online publication date: 1-Nov-2014
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Swan JKocsis ZLisitsa AArnold D(2014)The 'representative' metaheuristic design patternProceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation10.1145/2598394.2609842(1435-1436)Online publication date: 12-Jul-2014
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