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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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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DOI: https://doi.org/10.1007/s10589-007-9155-4