Gap-free computation of pareto-points by quadratic scalarizations
Gap-free computation of pareto-points by quadratic scalarizations
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.
multicriteria optimization, pareto-points, scalarization
69-89
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
February 2004
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Fliege, Jörg
(2004)
Gap-free computation of pareto-points by quadratic scalarizations.
Mathematical Methods of Operations Research, 59 (1), .
(doi:10.1007/s001860300316).
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.
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Published date: February 2004
Keywords:
multicriteria optimization, pareto-points, scalarization
Organisations:
Operational Research
Identifiers
Local EPrints ID: 48820
URI: http://eprints.soton.ac.uk/id/eprint/48820
ISSN: 1432-2994
PURE UUID: 47de967f-fbf2-42cc-a951-472d361f6d4c
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Date deposited: 15 Oct 2007
Last modified: 16 Mar 2024 03:57
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