Experiments with classification-based scalarizing functions in interactive multiobjective optimization

In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of...

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Published in:	European journal of operational research Vol. 175; no. 2; pp. 931 - 947
Main Authors:	Miettinen, Kaisa, Mäkelä, Marko M., Kaario, Katja
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.12.2006 Elsevier Elsevier Sequoia S.A
Series:	European Journal of Operational Research
Subjects:	Applied sciences Classification Exact sciences and technology Guaranteeing Pareto optimality Interactive methods Mathematical programming Multiple objective programming Operational research and scientific management Operational research. Management science Optimization Pareto optimum Studies Test problems Interactive methods Test problems Guaranteeing Pareto optimality Multiple objective programming Classification Pareto optimum Interactive mode Multiobjective programming Scalarization Guarantee Location problem Optimization
ISSN:	0377-2217, 1872-6860, 1872-6860
Online Access:	Get full text
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Abstract	In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this respect. We also collect a set of mostly nonlinear benchmark test problems that we use in the numerical comparisons.
AbstractList	In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this respect. We also collect a set of mostly nonlinear benchmark test problems that we use in the numerical comparisons. In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this respect. We also collect a set of mostly nonlinear benchmark test problems that we use in the numerical comparisons. [PUBLICATION ABSTRACT]
Author	Kaario, Katja Miettinen, Kaisa Mäkelä, Marko M.
Author_xml	– sequence: 1 givenname: Kaisa surname: Miettinen fullname: Miettinen, Kaisa email: miettine@hse.fi organization: Helsinki School of Economics, P.O. Box 1210, FI-00101 Helsinki, Finland – sequence: 2 givenname: Marko M. surname: Mäkelä fullname: Mäkelä, Marko M. email: makela@mit.jyu.fi organization: Department of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014 University of Jyväskylä, Finland – sequence: 3 givenname: Katja surname: Kaario fullname: Kaario, Katja email: kaario@mit.jyu.fi organization: Department of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014 University of Jyväskylä, Finland
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SubjectTerms	Applied sciences Classification Exact sciences and technology Guaranteeing Pareto optimality Interactive methods Mathematical programming Multiple objective programming Operational research and scientific management Operational research. Management science Optimization Pareto optimum Studies Test problems
Title	Experiments with classification-based scalarizing functions in interactive multiobjective optimization
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