Quadratic scalarization for decomposed multiobjective optimization

Brian Dandurand () and Margaret M. Wiecek
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Brian Dandurand: Clemson University
Margaret M. Wiecek: Clemson University

OR Spectrum: Quantitative Approaches in Management, 2016, vol. 38, issue 4, No 10, 1096 pages

Abstract: 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.

Keywords: Multiobjective optimization; Nonconvex optimization; Decomposition; Quadratic scalarization; Weighted-Chebyshev method (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00291-016-0453-z

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