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Reference Set Generator: A Method for Pareto Front Approximation and Reference Set Generation

Author

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  • Angel E. Rodriguez-Fernandez

    (Departmento de Computación, Centro de Investigación y de Estudios Avanzados del IPN, Mexico City 07360, Mexico)

  • Hao Wang

    (Leiden Institute of Advanced Computer Science and Applied Quantum Algorithms, Leiden University, 2311 EZ Leiden, The Netherlands)

  • Oliver Schütze

    (Departmento de Computación, Centro de Investigación y de Estudios Avanzados del IPN, Mexico City 07360, Mexico)

Abstract

In this paper, we address the problem of obtaining bias-free and complete finite size approximations of the solution sets (Pareto fronts) of multi-objective optimization problems (MOPs). Such approximations are, in particular, required for the fair usage of distance-based performance indicators, which are frequently used in evolutionary multi-objective optimization (EMO). If the Pareto front approximations are biased or incomplete, the use of these performance indicators can lead to misleading or false information. To address this issue, we propose the Reference Set Generator (RSG), which can, in principle, be applied to Pareto fronts of any shape and dimension. We finally demonstrate the strength of the novel approach on several benchmark problems.

Suggested Citation

  • Angel E. Rodriguez-Fernandez & Hao Wang & Oliver Schütze, 2025. "Reference Set Generator: A Method for Pareto Front Approximation and Reference Set Generation," Mathematics, MDPI, vol. 13(10), pages 1-28, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1626-:d:1656574
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    References listed on IDEAS

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    1. Günter Rudolph & Oliver Schütze & Christian Grimme & Christian Domínguez-Medina & Heike Trautmann, 2016. "Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results," Computational Optimization and Applications, Springer, vol. 64(2), pages 589-618, June.
    2. Hanne, Thomas, 1999. "On the convergence of multiobjective evolutionary algorithms," European Journal of Operational Research, Elsevier, vol. 117(3), pages 553-564, September.
    3. Beume, Nicola & Naujoks, Boris & Emmerich, Michael, 2007. "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1653-1669, September.
    4. 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.
    5. 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.
    6. Federico Zuiani & Massimiliano Vasile, 2013. "Multi Agent Collaborative Search based on Tchebycheff decomposition," Computational Optimization and Applications, Springer, vol. 56(1), pages 189-208, September.
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