A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem
Identifieur interne : 001569 ( Istex/Corpus ); précédent : 001568; suivant : 001570A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem
Auteurs : Nguyen V. ThoaiSource :
- European Journal of Operational Research [ 0377-2217 ] ; 2000.
Abstract
One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of efficient solutions. This is a very difficult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the efficient set is linear as well. In this article, we consider the problem of maximizing a special function over the efficient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.
Url:
DOI: 10.1016/S0377-2217(99)00068-5
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Thoai</name><affiliation><mods:affiliation>Department of Mathematics, University of Trier, 54286 Trier, Germany</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:8146A932CCE218E8BF251A9B293B518CF91EC5F1</idno><date when="2000" year="2000">2000</date><idno type="doi">10.1016/S0377-2217(99)00068-5</idno><idno type="url">https://api.istex.fr/document/8146A932CCE218E8BF251A9B293B518CF91EC5F1/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001569</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001569</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem</title><author><name sortKey="Thoai, Nguyen V" sort="Thoai, Nguyen V" uniqKey="Thoai N" first="Nguyen V." last="Thoai">Nguyen V. Thoai</name><affiliation><mods:affiliation>Department of Mathematics, University of Trier, 54286 Trier, Germany</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">European Journal of Operational Research</title><title level="j" type="abbrev">EOR</title><idno type="ISSN">0377-2217</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000">2000</date><biblScope unit="volume">122</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="58">58</biblScope><biblScope unit="page" to="68">68</biblScope></imprint><idno type="ISSN">0377-2217</idno></series><idno type="istex">8146A932CCE218E8BF251A9B293B518CF91EC5F1</idno><idno type="DOI">10.1016/S0377-2217(99)00068-5</idno><idno type="PII">S0377-2217(99)00068-5</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0377-2217</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of efficient solutions. This is a very difficult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the efficient set is linear as well. In this article, we consider the problem of maximizing a special function over the efficient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>Nguyen V. Thoai</name><affiliations><json:string>Department of Mathematics, University of Trier, 54286 Trier, Germany</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Multiple criteria optimization</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Optimization on efficient sets</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Global optimization</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Outer approximation algorithms</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of efficient solutions. This is a very difficult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the efficient set is linear as well. In this article, we consider the problem of maximizing a special function over the efficient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.</abstract><qualityIndicators><score>6.968</score><pdfVersion>1.2</pdfVersion><pdfPageSize>544 x 743 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>4</keywordCount><abstractCharCount>1055</abstractCharCount><pdfWordCount>6304</pdfWordCount><pdfCharCount>28185</pdfCharCount><pdfPageCount>11</pdfPageCount><abstractWordCount>164</abstractWordCount></qualityIndicators><title>A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem</title><pii><json:string>S0377-2217(99)00068-5</json:string></pii><refBibs><json:item><author><json:item><name>H.P. 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Tel.: +49-651-201-3475; fax: +49-651-201-3479; E-mail address: thoai@uni-trier.de.</p></note><affiliation>Department of Mathematics, University of Trier, 54286 Trier, Germany</affiliation></author></analytic><monogr><title level="j">European Journal of Operational Research</title><title level="j" type="abbrev">EOR</title><idno type="pISSN">0377-2217</idno><idno type="PII">S0377-2217(00)X0120-8</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000"></date><biblScope unit="volume">122</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="58">58</biblScope><biblScope unit="page" to="68">68</biblScope></imprint></monogr><idno type="istex">8146A932CCE218E8BF251A9B293B518CF91EC5F1</idno><idno type="DOI">10.1016/S0377-2217(99)00068-5</idno><idno type="PII">S0377-2217(99)00068-5</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2000</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of efficient solutions. This is a very difficult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the efficient set is linear as well. In this article, we consider the problem of maximizing a special function over the efficient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Multiple criteria optimization</term></item><item><term>Optimization on efficient sets</term></item><item><term>Global optimization</term></item><item><term>Outer approximation algorithms</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2000">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/8146A932CCE218E8BF251A9B293B518CF91EC5F1/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: ce:floats; body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>EOR</jid><aid>3849</aid><ce:pii>S0377-2217(99)00068-5</ce:pii><ce:doi>10.1016/S0377-2217(99)00068-5</ce:doi><ce:copyright year="2000" type="full-transfer">Elsevier Science B.V.</ce:copyright></item-info><head><ce:dochead><ce:textfn>Theory and Methodology</ce:textfn></ce:dochead><ce:title>A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem</ce:title><ce:author-group><ce:author><ce:given-name>Nguyen V.</ce:given-name><ce:surname>Thoai</ce:surname><ce:cross-ref refid="CORR1">*</ce:cross-ref></ce:author><ce:affiliation><ce:textfn>Department of Mathematics, University of Trier, 54286 Trier, Germany</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author. Tel.: +49-651-201-3475; fax: +49-651-201-3479; E-mail address: thoai@uni-trier.de.</ce:text></ce:correspondence></ce:author-group><ce:date-received day="20" month="7" year="1998"></ce:date-received><ce:date-accepted day="25" month="1" year="1999"></ce:date-accepted><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of efficient solutions. This is a very difficult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the efficient set is linear as well. In this article, we consider the problem of maximizing a special function over the efficient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Multiple criteria optimization</ce:text></ce:keyword><ce:keyword><ce:text>Optimization on efficient sets</ce:text></ce:keyword><ce:keyword><ce:text>Global optimization</ce:text></ce:keyword><ce:keyword><ce:text>Outer approximation algorithms</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem</title></titleInfo><name type="personal"><namePart type="given">Nguyen V.</namePart><namePart type="family">Thoai</namePart><affiliation>Department of Mathematics, University of Trier, 54286 Trier, Germany</affiliation><description>Corresponding author. Tel.: +49-651-201-3475; fax: +49-651-201-3479; E-mail address: thoai@uni-trier.de.</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">2000</dateIssued><copyrightDate encoding="w3cdtf">2000</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of efficient solutions. This is a very difficult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the efficient set is linear as well. In this article, we consider the problem of maximizing a special function over the efficient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.</abstract><note type="content">Section title: Theory and Methodology</note><note type="content">Table 1: Computational results on some typical test problems</note><subject><genre>Keywords</genre><topic>Multiple criteria optimization</topic><topic>Optimization on efficient sets</topic><topic>Global optimization</topic><topic>Outer approximation algorithms</topic></subject><relatedItem type="host"><titleInfo><title>European Journal of Operational Research</title></titleInfo><titleInfo type="abbreviated"><title>EOR</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">20000401</dateIssued></originInfo><identifier type="ISSN">0377-2217</identifier><identifier type="PII">S0377-2217(00)X0120-8</identifier><part><date>20000401</date><detail type="volume"><number>122</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="issue pages"><start>1</start><end>174</end></extent><extent unit="pages"><start>58</start><end>68</end></extent></part></relatedItem><identifier type="istex">8146A932CCE218E8BF251A9B293B518CF91EC5F1</identifier><identifier type="DOI">10.1016/S0377-2217(99)00068-5</identifier><identifier type="PII">S0377-2217(99)00068-5</identifier><accessCondition type="use and reproduction" contentType="copyright">©2000 Elsevier Science B.V.</accessCondition><recordInfo><recordContentSource>ELSEVIER</recordContentSource><recordOrigin>Elsevier Science B.V., ©2000</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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