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|Rank=2
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{{Inproceedings
 
{{Inproceedings
 
|Referiert=True
 
|Referiert=True
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|BibTex-ID=shukla2013indicator
 
|Title=Indicator Based Search in Variable Orderings: Theory and Algorithms
 
|Title=Indicator Based Search in Variable Orderings: Theory and Algorithms
 
|Year=2013
 
|Year=2013
|Booktitle=in EMO 2013
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|Booktitle=Evolutionary Multi-Criterion Optimization
|Publisher=Springer
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|Pages=66-80
|Series=LNCS
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|Publisher=Springer Berlin Heidelberg
|Number=in press
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|Editor=Purshouse, Robin C. and Fleming, Peter J. and Fonseca, Carlos M. and Greco, Salvatore and Shaw, Jane
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|Series=Lecture Notes in Computer Science
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|Volume=7811
 
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{{Publikation Details
 
{{Publikation Details
 
|Abstract=Various real world problems, especially in financial applications, medical engineering and game theory, involve solving a multi-objective optimization problem with a variable ordering structure. This means that the ordering relation  at a point in the (multi-)objective space depends on the point. This is a striking difference from usual multi-objective optimization problems, where the ordering is induced by the Pareto-cone and remains constant throughout the objective space. In addition to variability, in many applications (like portfolio optimization) the ordering is induced by a non-convex set instead of a cone. The main purpose of this paper is to provide theoretical and algorithmic advances for general set-based variable orderings. A hypervolume based indicator measure is also proposed for the first time, for such optimization tasks. Theoretical results are derived and properties of this indicator are studied. Moreover, the theory is also used to develop three indicator based algorithms for approximating the set of optimal solutions. Computational results show the niche of population based algorithms for solving multi-objective problems with variable orderings.
 
|Abstract=Various real world problems, especially in financial applications, medical engineering and game theory, involve solving a multi-objective optimization problem with a variable ordering structure. This means that the ordering relation  at a point in the (multi-)objective space depends on the point. This is a striking difference from usual multi-objective optimization problems, where the ordering is induced by the Pareto-cone and remains constant throughout the objective space. In addition to variability, in many applications (like portfolio optimization) the ordering is induced by a non-convex set instead of a cone. The main purpose of this paper is to provide theoretical and algorithmic advances for general set-based variable orderings. A hypervolume based indicator measure is also proposed for the first time, for such optimization tasks. Theoretical results are derived and properties of this indicator are studied. Moreover, the theory is also used to develop three indicator based algorithms for approximating the set of optimal solutions. Computational results show the niche of population based algorithms for solving multi-objective problems with variable orderings.
 +
|ISBN=978-3-642-37139-4
 +
|Link=http://dx.doi.org/10.1007/978-3-642-37140-0_9
 +
|DOI Name=10.1007/978-3-642-37140-0_9
 
|Forschungsgruppe=Effiziente Algorithmen
 
|Forschungsgruppe=Effiziente Algorithmen
 
}}
 
}}

Aktuelle Version vom 15. April 2015, 13:54 Uhr


Indicator Based Search in Variable Orderings: Theory and Algorithms


Indicator Based Search in Variable Orderings: Theory and Algorithms



Published: 2013
Herausgeber: Purshouse, Robin C. and Fleming, Peter J. and Fonseca, Carlos M. and Greco, Salvatore and Shaw, Jane
Buchtitel: Evolutionary Multi-Criterion Optimization
Ausgabe: 7811
Reihe: Lecture Notes in Computer Science
Seiten: 66-80
Verlag: Springer Berlin Heidelberg

Referierte Veröffentlichung

BibTeX

Kurzfassung
Various real world problems, especially in financial applications, medical engineering and game theory, involve solving a multi-objective optimization problem with a variable ordering structure. This means that the ordering relation at a point in the (multi-)objective space depends on the point. This is a striking difference from usual multi-objective optimization problems, where the ordering is induced by the Pareto-cone and remains constant throughout the objective space. In addition to variability, in many applications (like portfolio optimization) the ordering is induced by a non-convex set instead of a cone. The main purpose of this paper is to provide theoretical and algorithmic advances for general set-based variable orderings. A hypervolume based indicator measure is also proposed for the first time, for such optimization tasks. Theoretical results are derived and properties of this indicator are studied. Moreover, the theory is also used to develop three indicator based algorithms for approximating the set of optimal solutions. Computational results show the niche of population based algorithms for solving multi-objective problems with variable orderings.

ISBN: 978-3-642-37139-4
Weitere Informationen unter: Link
DOI Link: 10.1007/978-3-642-37140-0_9



Forschungsgruppe

Effiziente Algorithmen


Forschungsgebiet

Evolutionäre Algorithmen, Multikriterielle Optimierung, Globale Optimierung