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Covering Pareto Sets by Multilevel Subdivision Techniques

Author

Listed:
  • M. Dellnitz

    (University of Paderborn)

  • O. Schütze

    (University of Paderborn)

  • T. Hestermeyer

    (University of Paderborn)

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.

Suggested Citation

  • M. Dellnitz & O. Schütze & T. Hestermeyer, 2005. "Covering Pareto Sets by Multilevel Subdivision Techniques," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 113-136, January.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6468-7
    DOI: 10.1007/s10957-004-6468-7
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    Citations

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    Cited by:

    1. Lourdes Uribe & Johan M Bogoya & Andrés Vargas & Adriana Lara & Günter Rudolph & Oliver Schütze, 2020. "A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems," Mathematics, MDPI, vol. 8(10), pages 1-29, October.
    2. Bennet Gebken & Sebastian Peitz, 2021. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 696-723, March.
    3. Oliver Cuate & Oliver Schütze, 2020. "Pareto Explorer for Finding the Knee for Many Objective Optimization Problems," Mathematics, MDPI, vol. 8(10), pages 1-24, September.
    4. Farshad Noravesh & Kristiaan Kerstens, 2022. "Some connections between higher moments portfolio optimization methods," Papers 2201.00205, arXiv.org.
    5. Bennet Gebken & Sebastian Peitz & Michael Dellnitz, 2019. "On the hierarchical structure of Pareto critical sets," Journal of Global Optimization, Springer, vol. 73(4), pages 891-913, April.
    6. Carlos Ignacio Hernández Castellanos & Oliver Schütze & Jian-Qiao Sun & Guillermo Morales-Luna & Sina Ober-Blöbaum, 2020. "Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    7. Clempner, Julio B. & Poznyak, Alexander S., 2016. "Solving the Pareto front for multiobjective Markov chains using the minimum Euclidean distance gradient-based optimization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 142-160.
    8. Oliver Cuate & Antonin Ponsich & Lourdes Uribe & Saúl Zapotecas-Martínez & Adriana Lara & Oliver Schütze, 2019. "A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs," Mathematics, MDPI, vol. 8(1), pages 1-25, December.
    9. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    10. Paritosh Jha & Marco Cucculelli, 2023. "Enhancing the predictive performance of ensemble models through novel multi-objective strategies: evidence from credit risk and business model innovation survey data," Annals of Operations Research, Springer, vol. 325(2), pages 1029-1047, June.
    11. Johan M. Bogoya & Andrés Vargas & Oliver Schütze, 2019. "The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review," Mathematics, MDPI, vol. 7(10), pages 1-35, September.

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