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Quadratic scalarization for decomposed multiobjective optimization

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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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Acknowledgments

The views presented in this work do not necessarily represent the views of our sponsors, the Automotive Research Center, a center of excellence of the US Army TACOM, and the National Science Foundation, Grant number CMMI-1129969, whose support is greatly appreciated.Furthermore, we are very grateful to the anonymous referees, whose thorough review and helpful comments aided us considerably in improving this manuscript.

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  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, USA

    Brian Dandurand & Margaret M. Wiecek

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  1. Brian Dandurand
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  2. Margaret M. Wiecek
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Correspondence to Brian Dandurand.

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Dandurand, B., Wiecek, M.M. Quadratic scalarization for decomposed multiobjective optimization. OR Spectrum 38, 1071–1096 (2016). https://doi.org/10.1007/s00291-016-0453-z

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