Approximability and Hardness in Multi-objective Optimization
Identifieur interne : 001017 ( Istex/Corpus ); précédent : 001016; suivant : 001018Approximability and Hardness in Multi-objective Optimization
Auteurs : Christian Gla Er ; Christian Reitwie Ner ; Heinz Schmitz ; Maximilian WitekSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Url:
DOI: 10.1007/978-3-642-13962-8_20
Links to Exploration step
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<notesStmt><note type="content">We define and compare several solution notions that capture reasonable algorithmic tasks for computing optimal solutions.</note>
<note type="content">These solution notions induce corresponding NP-hardness notions for which we prove implication and separation results.</note>
<note type="content">We define approximative solution notions and investigate in which cases polynomial-time solvability translates from one to another notion. Moreover, for problems where all objectives have to be minimized, approximability results translate from single-objective to multi-objective optimization such that the relative error degrades only by a constant factor. Such translations are not possible for problems where all objectives have to be maximized (unless P = NP).</note>
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<ChapterTitle Language="En">Approximability and Hardness in Multi-objective Optimization</ChapterTitle>
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<Para>We study the approximability and the hardness of combinatorial multi-objective NP optimization problems (multi-objective problems, for short). Our contributions are:</Para>
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<ItemContent><Para>These solution notions induce corresponding NP-hardness notions for which we prove implication and separation results.</Para>
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<ItemContent><Para>We define approximative solution notions and investigate in which cases polynomial-time solvability translates from one to another notion. Moreover, for problems where all objectives have to be minimized, approximability results translate from single-objective to multi-objective optimization such that the relative error degrades only by a constant factor. Such translations are not possible for problems where all objectives have to be maximized (unless P = NP).</Para>
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<Para>As a consequence we see that in contrast to single-objective problems (where the solution notions coincide), the situation is more subtle for multiple objectives. So it is important to exactly specify the NP-hardness notion when discussing the complexity of multi-objective problems.</Para>
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<note type="content">We define and compare several solution notions that capture reasonable algorithmic tasks for computing optimal solutions.</note>
<note type="content">These solution notions induce corresponding NP-hardness notions for which we prove implication and separation results.</note>
<note type="content">We define approximative solution notions and investigate in which cases polynomial-time solvability translates from one to another notion. Moreover, for problems where all objectives have to be minimized, approximability results translate from single-objective to multi-objective optimization such that the relative error degrades only by a constant factor. Such translations are not possible for problems where all objectives have to be maximized (unless P = NP).</note>
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<name type="personal"><namePart type="given">Elvira</namePart>
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<name type="personal"><namePart type="given">Luís</namePart>
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<affiliation>Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal</affiliation>
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<namePart type="family">Hutchison</namePart>
<affiliation>Lancaster University, Lancaster, UK</affiliation>
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<name type="personal"><namePart type="given">Takeo</namePart>
<namePart type="family">Kanade</namePart>
<affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation>
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</name>
<name type="personal"><namePart type="given">Josef</namePart>
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<affiliation>University of Surrey, Guildford, UK</affiliation>
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<name type="personal"><namePart type="given">Jon</namePart>
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<namePart type="family">Kleinberg</namePart>
<affiliation>Cornell University, Ithaca, NY, USA</affiliation>
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<name type="personal"><namePart type="given">Friedemann</namePart>
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<name type="personal"><namePart type="given">Moni</namePart>
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<name type="personal"><namePart type="given">Oscar</namePart>
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<name type="personal"><namePart type="given">Bernhard</namePart>
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<name type="personal"><namePart type="given">Demetri</namePart>
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<name type="personal"><namePart type="given">Doug</namePart>
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<name type="personal"><namePart type="given">Moshe</namePart>
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<affiliation>Rice University, Houston, TX, USA</affiliation>
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<name type="personal"><namePart type="given">Gerhard</namePart>
<namePart type="family">Weikum</namePart>
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