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Scalarizations for adaptively solving multi-objective optimization problems

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Abstract

In this paper several parameter dependent scalarization approaches for solving nonlinear multi-objective optimization problems are discussed. It is shown that they can be considered as special cases of a scalarization problem by Pascoletti and Serafini (or a modification of this problem).

Based on these connections theoretical results as well as a new algorithm for adaptively controlling the choice of the parameters for generating almost equidistant approximations of the efficient set, lately developed for the Pascoletti-Serafini scalarization, can be applied to these problems. For instance for such well-known scalarizations as the ε-constraint or the normal boundary intersection problem algorithms for adaptively generating high quality approximations are derived.

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  1. Institute of Applied Mathematics, University of Erlangen-Nürnberg, Martensstr. 3, 91058, Erlangen, Germany

    Gabriele Eichfelder

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  1. Gabriele Eichfelder
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Eichfelder, G. Scalarizations for adaptively solving multi-objective optimization problems. Comput Optim Appl 44, 249–273 (2009). https://doi.org/10.1007/s10589-007-9155-4

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