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- Publisher Website: 10.1162/evco_a_00249
- Scopus: eid_2-s2.0-85080123048
- PMID: 30721086
- WOS: WOS:000518638100003
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Article: A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems
Title | A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems |
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Authors | |
Keywords | Convergence in distribution Evolutionary algorithms Infinite population models Population dynamics Theoretical analysis |
Issue Date | 2019 |
Publisher | MIT Press. The Journal's web site is located at https://www.mitpressjournals.org/loi/evco |
Citation | Evolutionary Computation, 2019, v. 28 n. 1, p. 55-85 How to Cite? |
Abstract | Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models are derived from Markov chains by exploiting symmetries between individuals in the population and analyzing the limit as the population size goes to infinity. In this article, we study the theoretical foundations of infinite population models of evolutionary algorithms on continuous optimization problems. First, we show that the convergence proofs in a widely cited study were in fact problematic and incomplete. We further show that the modeling assumption of exchangeability of individuals cannot yield the transition equation. Then, in order to analyze infinite population models, we build an analytical framework based on convergence in distribution of random elements which take values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It also provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Finally, we use the framework to prove the convergence of infinite population models for the mutation operator and the k-ary recombination operator. We show that these operators can provide accurate predictions for real population dynamics as the population size goes to infinity, provided that the initial population is identically and independently distributed. |
Persistent Identifier | http://hdl.handle.net/10722/275007 |
ISSN | 2023 Impact Factor: 4.6 2023 SCImago Journal Rankings: 1.170 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Song, B | - |
dc.contributor.author | Li, VOK | - |
dc.date.accessioned | 2019-09-10T02:33:31Z | - |
dc.date.available | 2019-09-10T02:33:31Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Evolutionary Computation, 2019, v. 28 n. 1, p. 55-85 | - |
dc.identifier.issn | 1063-6560 | - |
dc.identifier.uri | http://hdl.handle.net/10722/275007 | - |
dc.description.abstract | Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models are derived from Markov chains by exploiting symmetries between individuals in the population and analyzing the limit as the population size goes to infinity. In this article, we study the theoretical foundations of infinite population models of evolutionary algorithms on continuous optimization problems. First, we show that the convergence proofs in a widely cited study were in fact problematic and incomplete. We further show that the modeling assumption of exchangeability of individuals cannot yield the transition equation. Then, in order to analyze infinite population models, we build an analytical framework based on convergence in distribution of random elements which take values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It also provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Finally, we use the framework to prove the convergence of infinite population models for the mutation operator and the k-ary recombination operator. We show that these operators can provide accurate predictions for real population dynamics as the population size goes to infinity, provided that the initial population is identically and independently distributed. | - |
dc.language | eng | - |
dc.publisher | MIT Press. The Journal's web site is located at https://www.mitpressjournals.org/loi/evco | - |
dc.relation.ispartof | Evolutionary Computation | - |
dc.rights | Evolutionary Computation. Copyright © MIT Press. | - |
dc.subject | Convergence in distribution | - |
dc.subject | Evolutionary algorithms | - |
dc.subject | Infinite population models | - |
dc.subject | Population dynamics | - |
dc.subject | Theoretical analysis | - |
dc.title | A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems | - |
dc.type | Article | - |
dc.identifier.email | Li, VOK: vli@eee.hku.hk | - |
dc.identifier.authority | Li, VOK=rp00150 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1162/evco_a_00249 | - |
dc.identifier.pmid | 30721086 | - |
dc.identifier.scopus | eid_2-s2.0-85080123048 | - |
dc.identifier.hkuros | 302910 | - |
dc.identifier.volume | 28 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 55 | - |
dc.identifier.epage | 85 | - |
dc.identifier.isi | WOS:000518638100003 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 1063-6560 | - |