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A parallel multiple reference point approach for multi-objective optimization

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  • Figueira, J.R.
  • Liefooghe, A.
  • Talbi, E.-G.
  • Wierzbicki, A.P.

Abstract

This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed within a region that covers the Pareto Frontier. An evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space. Computational experiments are performed on a bi-objective flow-shop scheduling problem. Results, quality measures as well as a statistical analysis are reported in the paper.

Suggested Citation

  • Figueira, J.R. & Liefooghe, A. & Talbi, E.-G. & Wierzbicki, A.P., 2010. "A parallel multiple reference point approach for multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 205(2), pages 390-400, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:2:p:390-400
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    2. Yannik Zeiträg & José Rui Figueira, 2023. "Automatically evolving preference-based dispatching rules for multi-objective job shop scheduling," Journal of Scheduling, Springer, vol. 26(3), pages 289-314, June.
    3. Li, Wei & Nault, Barrie R. & Ye, Honghan, 2019. "Trade-off balancing in scheduling for flow shop production and perioperative processes," European Journal of Operational Research, Elsevier, vol. 273(3), pages 817-830.
    4. Steuer, Ralph E. & Utz, Sebastian, 2023. "Non-contour efficient fronts for identifying most preferred portfolios in sustainability investing," European Journal of Operational Research, Elsevier, vol. 306(2), pages 742-753.
    5. Pinto, F.S. & Figueira, J.R. & Marques, R.C., 2015. "A multi-objective approach with soft constraints for water supply and wastewater coverage improvements," European Journal of Operational Research, Elsevier, vol. 246(2), pages 609-618.
    6. 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.
    7. Liefooghe, Arnaud & Jourdan, Laetitia & Talbi, El-Ghazali, 2011. "A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO," European Journal of Operational Research, Elsevier, vol. 209(2), pages 104-112, March.
    8. Theodor J. Stewart, 2016. "Multiple objective project portfolio selection based on reference points," Journal of Business Economics, Springer, vol. 86(1), pages 23-33, January.
    9. Liang, Wen Yau & Huang, Chun-Che & Lin, Yin-Chen & Chang, Tsun Hsien & Shih, Meng Hao, 2013. "The multi-objective label correcting algorithm for supply chain modeling," International Journal of Production Economics, Elsevier, vol. 142(1), pages 172-178.
    10. Lakmali Weerasena & Aniekan Ebiefung & Anthony Skjellum, 2022. "Design of a heuristic algorithm for the generalized multi-objective set covering problem," Computational Optimization and Applications, Springer, vol. 82(3), pages 717-751, July.
    11. Cem P. Cetinkaya & Mert Can Gunacti, 2018. "Multi-Criteria Analysis of Water Allocation Scenarios in a Water Scarce Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(8), pages 2867-2884, June.
    12. Derbel, Bilel & Humeau, Jérémie & Liefooghe, Arnaud & Verel, Sébastien, 2014. "Distributed localized bi-objective search," European Journal of Operational Research, Elsevier, vol. 239(3), pages 731-743.
    13. Sahinkoc, H. Mert & Bilge, Ümit, 2022. "A reference set based many-objective co-evolutionary algorithm with an application to the knapsack problem," European Journal of Operational Research, Elsevier, vol. 300(2), pages 405-417.
    14. E. Filatovas & O. Kurasova & J. L. Redondo & J. Fernández, 2020. "A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 402-423, July.
    15. Schryen, Guido, 2020. "Parallel computational optimization in operations research: A new integrative framework, literature review and research directions," European Journal of Operational Research, Elsevier, vol. 287(1), pages 1-18.

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