A Convergence Indicator for Multi-Objective Optimisation Algorithms
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300437 |
Resumo: | ABSTRACT The algorithms of multi-objective optimisation had a relative growth in the last years. Thereby, it requires some way of comparing the results of these. In this sense, performance measures play a key role. In general, it’s considered some properties of these algorithms such as capacity, convergence, diversity or convergence-diversity. There are some known measures such as generational distance (GD), inverted generational distance (IGD), hypervolume (HV), Spread (∆), Averaged Hausdorff distance (∆ p ), R2-indicator, among others. In this paper, we focuses on proposing a new indicator to measure convergence based on the traditional formula for Shannon entropy. The main features about this measure are: 1) It does not require to know the true Pareto set and 2) Medium computational cost when compared with Hypervolume. |
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A Convergence Indicator for Multi-Objective Optimisation AlgorithmsShannon EntropyPerformance MeasureMulti-Objective Optimisation AlgorithmsABSTRACT The algorithms of multi-objective optimisation had a relative growth in the last years. Thereby, it requires some way of comparing the results of these. In this sense, performance measures play a key role. In general, it’s considered some properties of these algorithms such as capacity, convergence, diversity or convergence-diversity. There are some known measures such as generational distance (GD), inverted generational distance (IGD), hypervolume (HV), Spread (∆), Averaged Hausdorff distance (∆ p ), R2-indicator, among others. In this paper, we focuses on proposing a new indicator to measure convergence based on the traditional formula for Shannon entropy. The main features about this measure are: 1) It does not require to know the true Pareto set and 2) Medium computational cost when compared with Hypervolume.Sociedade Brasileira de Matemática Aplicada e Computacional2018-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300437TEMA (São Carlos) v.19 n.3 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.03.0437info:eu-repo/semantics/openAccessSANTOS,T.XAVIER,S.eng2018-12-13T00:00:00Zoai:scielo:S2179-84512018000300437Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-12-13T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse |
dc.title.none.fl_str_mv |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
title |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
spellingShingle |
A Convergence Indicator for Multi-Objective Optimisation Algorithms SANTOS,T. Shannon Entropy Performance Measure Multi-Objective Optimisation Algorithms |
title_short |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
title_full |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
title_fullStr |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
title_full_unstemmed |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
title_sort |
A Convergence Indicator for Multi-Objective Optimisation Algorithms |
author |
SANTOS,T. |
author_facet |
SANTOS,T. XAVIER,S. |
author_role |
author |
author2 |
XAVIER,S. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
SANTOS,T. XAVIER,S. |
dc.subject.por.fl_str_mv |
Shannon Entropy Performance Measure Multi-Objective Optimisation Algorithms |
topic |
Shannon Entropy Performance Measure Multi-Objective Optimisation Algorithms |
description |
ABSTRACT The algorithms of multi-objective optimisation had a relative growth in the last years. Thereby, it requires some way of comparing the results of these. In this sense, performance measures play a key role. In general, it’s considered some properties of these algorithms such as capacity, convergence, diversity or convergence-diversity. There are some known measures such as generational distance (GD), inverted generational distance (IGD), hypervolume (HV), Spread (∆), Averaged Hausdorff distance (∆ p ), R2-indicator, among others. In this paper, we focuses on proposing a new indicator to measure convergence based on the traditional formula for Shannon entropy. The main features about this measure are: 1) It does not require to know the true Pareto set and 2) Medium computational cost when compared with Hypervolume. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-12-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300437 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300437 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.5540/tema.2018.019.03.0437 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
TEMA (São Carlos) v.19 n.3 2018 reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) instname:Sociedade Brasileira de Matemática Aplicada e Computacional instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) |
collection |
TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) |
repository.name.fl_str_mv |
TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional |
repository.mail.fl_str_mv |
castelo@icmc.usp.br |
_version_ |
1752122220530892800 |