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On Continuation Methods for the Numerical Treatment of Multi-Objective Optimization Problems

Authors: Oliver Schütze, Alessandro Dell'Aere, and Michael Dellnitz

Published in: Dagstuhl Seminar Proceedings, Volume 4461, Practical Approaches to Multi-Objective Optimization (2005)

Abstract

In this report we describe how continuation methods can be used for the numerical treatment of multi-objective optimization problems (MOPs): starting with a given Karush-Kuhn-Tucker point (KKT-point) x of an MOP, these techniques can be applied to detect further KKT-points in the neighborhood of x. In the next step, again further points are computed starting with these new-found KKT-points, and so on. In order to maintain a good spread of these solutions we use boxes for the representation of the computed parts of the solution set. Based on this background, we propose a new predictor-corrector variant, and show some numerical results indicating the strength of the method, in particular in higher dimensions. Further, the data structure allows for an efficient computation of MOPs with more than two objectives, which has not been considered so far in most existing continuation methods.

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Oliver Schütze, Alessandro Dell'Aere, and Michael Dellnitz. On Continuation Methods for the Numerical Treatment of Multi-Objective Optimization Problems. In Practical Approaches to Multi-Objective Optimization. Dagstuhl Seminar Proceedings, Volume 4461, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{schutze_et_al:DagSemProc.04461.16,
  author =	{Sch\"{u}tze, Oliver and Dell'Aere, Alessandro and Dellnitz, Michael},
  title =	{{On Continuation Methods for the Numerical Treatment of Multi-Objective Optimization Problems}},
  booktitle =	{Practical Approaches to Multi-Objective Optimization},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4461},
  editor =	{J\"{u}rgen Branke and Kalyanmoy Deb and Kaisa Miettinen and Ralph E. Steuer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04461.16},
  URN =		{urn:nbn:de:0030-drops-3497},
  doi =		{10.4230/DagSemProc.04461.16},
  annote =	{Keywords: multi-objective optimization, continuation, k-manifolds}
}

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On Continuation Methods for the Numerical Treatment of Multi-Objective Optimization Problems

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