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OR Spectrum
Published in: OR Spectrum 4/2016

01-10-2016 | Regular Article

Quadratic scalarization for decomposed multiobjective optimization

Authors: Brian Dandurand, Margaret M. Wiecek

Published in: OR Spectrum | Issue 4/2016

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Abstract

Practical applications in multidisciplinary engineering design, business management, and military planning require distributed solution approaches for solving nonconvex, multiobjective optimization problems (MOPs). Under this motivation, a quadratic scalarization method (QSM) is developed with the goal to preserve decomposable structures of the MOP while addressing nonconvexity in a manner that avoids a high degree of nonlinearity and the introduction of additional nonsmoothness. Under certain assumptions, necessary and sufficient conditions for QSM-generated solutions to be weakly and properly efficient for an MOP are developed, with any form of efficiency being understood in a local sense. QSM is shown to correspond with the relaxed, reformulated weighted-Chebyshev method as a special case. An example is provided for demonstrating the application of QSM to a nonconvex MOP.
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Metadata
Title
Quadratic scalarization for decomposed multiobjective optimization
Authors
Brian Dandurand
Margaret M. Wiecek
Publication date
01-10-2016
Publisher
Springer Berlin Heidelberg
Published in
OR Spectrum / Issue 4/2016
Print ISSN: 0171-6468
Electronic ISSN: 1436-6304
DOI
https://doi.org/10.1007/s00291-016-0453-z

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