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Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search

In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems

Author

Listed:
  • Kalyanmoy Deb

    (Indian Institute of Technology Kanpur
    Helsinki School of Economics)

  • Kaisa Miettinen

Abstract

Estimation of the nadir objective vector representing worst objective function values in the set of Pareto-optimal solutions is an important task, particularly for multi-objective optimization problems having more than two conflicting objectives. Along with the ideal point, nadir point can be used to normalize the objectives so that multi-objective optimization algorithms can be used more reliably. The knowledge of the nadir point is also a pre-requisite to many multiple criteria decision making methodologies. Moreover, nadir point is useful for an aid in interactive methodologies and visualization softwares catered for multi-objective optimization. However, the computation of an exact nadir point for more than two objectives is not an easy matter, simply because the nadir point demands the knowledge of extreme Pareto-optimal solutions. In the past few years, researchers have proposed several nadir point estimation procedures using evolutionary optimization methodologies. In this paper, we review the past studies and reveal an interesting chronicle of events in this direction. To make the estimation procedure computationally faster and more accurate, the methodologies were refined one after the other by mainly focusing on finding smaller and still sufficient subset of Pareto-optimal solutions to facilitate estimating the nadir point. Simulation results on a number of numerical test problems demonstrate better efficacy of the approach which aims to find only the extreme Pareto-optimal points compared to other two approaches.

Suggested Citation

  • Kalyanmoy Deb & Kaisa Miettinen, 2010. "Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 339-354, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-04045-0_29
    DOI: 10.1007/978-3-642-04045-0_29
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    Citations

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    Cited by:

    1. Francisco Ruiz & Mariano Luque & Kaisa Miettinen, 2012. "Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization," Annals of Operations Research, Springer, vol. 197(1), pages 47-70, August.
    2. Ana Ruiz & Rubén Saborido & Mariano Luque, 2015. "A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm," Journal of Global Optimization, Springer, vol. 62(1), pages 101-129, May.
    3. Mariano Luque & Ana Ruiz & Rubén Saborido & Óscar Marcenaro-Gutiérrez, 2015. "On the use of the $$L_{p}$$ L p distance in reference point-based approaches for multiobjective optimization," Annals of Operations Research, Springer, vol. 235(1), pages 559-579, December.
    4. Yadav, Deepanshu & Nagar, Deepak & Ramu, Palaniappan & Deb, Kalyanmoy, 2023. "Visualization-aided multi-criteria decision-making using interpretable self-organizing maps," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1183-1200.
    5. Miettinen, Kaisa & Eskelinen, Petri & Ruiz, Francisco & Luque, Mariano, 2010. "NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point," European Journal of Operational Research, Elsevier, vol. 206(2), pages 426-434, October.
    6. Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    7. O. D. Marcenaro-Gutierrez & M. Luque & L. A. Lopez-Agudo, 2016. "Balancing Teachers’ Math Satisfaction and Other Indicators of the Education System’s Performance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(3), pages 1319-1348, December.
    8. Ana B. Ruiz & Rubén Saborido & José D. Bermúdez & Mariano Luque & Enriqueta Vercher, 2020. "Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences," Journal of Global Optimization, Springer, vol. 76(2), pages 295-315, February.
    9. Ruiz, Ana B. & Sindhya, Karthik & Miettinen, Kaisa & Ruiz, Francisco & Luque, Mariano, 2015. "E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method," European Journal of Operational Research, Elsevier, vol. 246(1), pages 218-231.
    10. Benítez-Fernández, Amalia & Ruiz, Francisco, 2020. "A Meta-Goal Programming approach to cardinal preferences aggregation in multicriteria problems," Omega, Elsevier, vol. 94(C).

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