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Continuous Multiobjective Programming

In: Multiple Criteria Decision Analysis

Author

Listed:
  • Margaret M. Wiecek

    (Clemson University)

  • Matthias Ehrgott

    (Lancaster University)

  • Alexander Engau

    (Dalhousie University
    University of Colorado Denver)

Abstract

We present our view of the state of the art in continuous multiobjective programming. After an introduction we formulate the multiobjective program (MOP) and define the most important solution concepts in Sect. 18.2. In Sect. 18.3 we summarize properties of efficient and nondominated sets. Optimality conditions are reviewed in Sect. 18.4. The main part of the chapter consists of Sects. 18.5 and 18.6 that deal with solution techniques for MOPs and approximation of efficient and nondominated sets. In Sect. 18.7 we discuss specially-structured problems including linear, nonlinear, parametric, and bilevel MOPs. In Sect. 18.8 we present our perspective on future research directions.

Suggested Citation

  • Margaret M. Wiecek & Matthias Ehrgott & Alexander Engau, 2016. "Continuous Multiobjective Programming," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 739-815, Springer.
    • Handle: RePEc:spr:isochp:978-1-4939-3094-4_18
    DOI: 10.1007/978-1-4939-3094-4_18
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    Citations

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    Cited by:

    1. Finke, Jonas & Bertsch, Valentin, 2023. "Implementing a highly adaptable method for the multi-objective optimisation of energy systems," Applied Energy, Elsevier, vol. 332(C).
    2. Guillermo Cabrera-Guerrero & Andrew J. Mason & Andrea Raith & Matthias Ehrgott, 2018. "Pareto local search algorithms for the multi-objective beam angle optimisation problem," Journal of Heuristics, Springer, vol. 24(2), pages 205-238, April.
    3. Luciano Ferreira Cruz & Flavia Bernardo Pinto & Lucas Camilotti & Angelo Marcio Oliveira Santanna & Roberto Zanetti Freire & Leandro Santos Coelho, 2022. "Improved multiobjective differential evolution with spherical pruning algorithm for optimizing 3D printing technology parametrization process," Annals of Operations Research, Springer, vol. 319(2), pages 1565-1587, December.
    4. Finke, Jonas & Bertsch, Valentin, 2022. "Implementing a highly adaptable method for the multi-objective optimisation of energy systems," MPRA Paper 115504, University Library of Munich, Germany.
    5. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.
    6. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Other publications TiSEM 795b6c0c-c7bc-4ced-9d6b-a, Tilburg University, School of Economics and Management.
    7. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
    8. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    9. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Discussion Paper 2023-012, Tilburg University, Center for Economic Research.
    10. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    11. Pubudu L. W. Jayasekara & Andrew C. Pangia & Margaret M. Wiecek, 2023. "On solving parametric multiobjective quadratic programs with parameters in general locations," Annals of Operations Research, Springer, vol. 320(1), pages 123-172, January.
    12. C. P. Brás & A. L. Custódio, 2020. "On the use of polynomial models in multiobjective directional direct search," Computational Optimization and Applications, Springer, vol. 77(3), pages 897-918, December.
    13. Kalyan Shankar Bhattacharjee & Hemant Kumar Singh & Tapabrata Ray, 2017. "An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making," Journal of Global Optimization, Springer, vol. 68(1), pages 71-93, May.

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