article

Covering Pareto Sets by Multilevel Subdivision Techniques

Authors:

T. HestermeyerAuthors Info & Claims

Journal of Optimization Theory and Applications, Volume 124, Issue 1

Pages 113 - 136

https://doi.org/10.1007/s10957-004-6468-7

Published: 01 January 2005 Publication History

Abstract

In this work, we present a new set-oriented numerical method for the numerical solution of multiobjective optimization problems. These methods are global in nature and allow to approximate the entire set of (global) Pareto points. After proving convergence of an associated abstract subdivision procedure, we use this result as a basis for the development of three different algorithms. We consider also appropriate combinations of them in order to improve the total performance. Finally, we illustrate the efficiency of these techniques via academic examples plus a real technical application, namely, the optimization of an active suspension system for cars.

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Cited By

Gao KXu L(2024)A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategyApplied Soft Computing10.1016/j.asoc.2024.112022165:COnline publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1016/j.asoc.2024.112022
Wei TLiu JGupta ATan POng Y(2024)Bayesian Forward-Inverse Transfer for Multiobjective OptimizationParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70085-9_9(135-152)Online publication date: 14-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-70085-9_9
Gebken BPeitz S(2021)An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization ProblemsJournal of Optimization Theory and Applications10.1007/s10957-020-01803-w188:3(696-723)Online publication date: 13-Jan-2021
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cover image Journal of Optimization Theory and Applications

Journal of Optimization Theory and Applications Volume 124, Issue 1

January 2005

250 pages

ISSN:0022-3239

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Copyright © Copyright © 2005 Springer Science+Business Media, Inc.

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Plenum Press

United States

Publication History

Published: 01 January 2005

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Cited By

Gao KXu L(2024)A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategyApplied Soft Computing10.1016/j.asoc.2024.112022165:COnline publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1016/j.asoc.2024.112022
Wei TLiu JGupta ATan POng Y(2024)Bayesian Forward-Inverse Transfer for Multiobjective OptimizationParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70085-9_9(135-152)Online publication date: 14-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-70085-9_9
Gebken BPeitz S(2021)An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization ProblemsJournal of Optimization Theory and Applications10.1007/s10957-020-01803-w188:3(696-723)Online publication date: 13-Jan-2021
https://dl.acm.org/doi/10.1007/s10957-020-01803-w
Lovison AMiettinen K(2021)On the Extension of the DIRECT Algorithm to Multiple ObjectivesJournal of Global Optimization10.1007/s10898-020-00942-879:2(387-412)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s10898-020-00942-8
Wu XZhang SGong ZJi JLin QChen J(2020)Decomposition-Based Multiobjective Evolutionary Optimization with Adaptive Multiple Gaussian Process ModelsComplexity10.1155/2020/96432732020Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1155/2020/9643273
Qin ZXin YSun J(2020)Multi‐objective optimal motion control of a laboratory helicopter based on parallel simple cell mapping methodAsian Journal of Control10.1002/asjc.204022:4(1565-1578)Online publication date: 6-Jul-2020
https://dl.acm.org/doi/10.1002/asjc.2040
Gebken BPeitz SDellnitz M(2019)On the hierarchical structure of Pareto critical setsJournal of Global Optimization10.1007/s10898-019-00737-673:4(891-913)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s10898-019-00737-6
Peitz SOber-Blöbaum SDellnitz M(2019)Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order ModelingActa Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications10.1007/s10440-018-0209-7161:1(171-199)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s10440-018-0209-7
Rieger J(2019)Provably convergent implementations of the subdivision algorithm for the computation of invariant objectsNumerische Mathematik10.1007/s00211-018-0997-8142:1(149-165)Online publication date: 1-May-2019
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Emmerich MDeutz A(2018)A tutorial on multiobjective optimizationNatural Computing: an international journal10.1007/s11047-018-9685-y17:3(585-609)Online publication date: 1-Sep-2018
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