Scalarizations for adaptively solving multi-objective optimization problems

Authors:
Gabriele Eichfelder
Affiliations:
Institute of Applied Mathematics, University of Erlangen-Nürnberg, Erlangen, Germany 91058
Venue:
Computational Optimization and Applications
Year:
2009

Citing 5
Cited 1

Continuous dependence of solutions on a parameter in a scalarization method

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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 驴-constraint or the normal boundary intersection problem algorithms for adaptively generating high quality approximations are derived.