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Two-Sided Pareto Front Approximations

Author

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  • I. Kaliszewski

    (Polish Academy of Sciences)

  • J. Miroforidis

    (Polish Academy of Sciences
    Treeffect Co)

Abstract

A new approach to derive Pareto front approximations with evolutionary computations is proposed here. At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. However, accuracy of such approximations is known only if the Pareto front is known, which makes their usefulness questionable. Here we propose to exploit also elements outside feasible sets to derive pairs of such Pareto front approximations that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between elements of a pair. A rudimentary algorithm to derive pairs of Pareto front approximations is presented and the viability of the idea is verified on a limited number of test problems.

Suggested Citation

  • I. Kaliszewski & J. Miroforidis, 2014. "Two-Sided Pareto Front Approximations," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 845-855, September.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:3:d:10.1007_s10957-013-0498-y
    DOI: 10.1007/s10957-013-0498-y
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    References listed on IDEAS

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    1. Kaliszewski, Ignacy & Miroforidis, Janusz & Podkopaev, Dmitry, 2012. "Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy," European Journal of Operational Research, Elsevier, vol. 216(1), pages 188-199.
    2. Hanne, Thomas, 2007. "A multiobjective evolutionary algorithm for approximating the efficient set," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1723-1734, February.
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    Cited by:

    1. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.
    2. Janusz Miroforidis, 2021. "Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems," Journal of Global Optimization, Springer, vol. 80(3), pages 617-634, July.
    3. I. Kaliszewski & J. Miroforidis, 2021. "Cooperative multiobjective optimization with bounds on objective functions," Journal of Global Optimization, Springer, vol. 79(2), pages 369-385, February.
    4. I. Kaliszewski & J. Miroforidis, 2022. "Probing the Pareto front of a large-scale multiobjective problem with a MIP solver," Operational Research, Springer, vol. 22(5), pages 5617-5673, November.

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