Gap-free computation of pareto-points by quadratic scalarizations


Fliege, Jörg (2004) Gap-free computation of pareto-points by quadratic scalarizations. Mathematical Methods of Operations Research, 59, (1), 69-89. (doi:10.1007/s001860300316).

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Original Publication URL: http://dx.doi.org/10.1007/s001860300316

Description/Abstract

In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, approximations to the whole solution set are of particular importance to decision makers. Usually, approximating this set involves solving a family of parameterized optimization problems. It is the aim of this paper to argue in favour of parameterized quadratic objective functions, in contrast to the standard weighting approach in which parameterized linear objective functions are used. These arguments will rest on the favourable numerical properties of these quadratic scalarizations, which will be investigated in detail. Moreover, it will be shown which parameter sets can be used to recover all solutions of an original multiobjective problem where the ordering in the image space is induced by an arbitrary convex cone.

Item Type: Article
ISSNs: 1432-2994 (print)
Related URLs:
Keywords: multicriteria optimization, pareto-points, scalarization
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 48820
Date Deposited: 15 Oct 2007
Last Modified: 27 Mar 2014 18:32
URI: http://eprints.soton.ac.uk/id/eprint/48820

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