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$$\gamma $$ γ -Competitiveness

Author

Listed:
  • Ilgam Latypov

    (Lomonosov Moscow State University
    Moscow Institute of Physics and Technology)

  • Dorn Yuriy

    (Lomonosov Moscow State University
    Moscow Institute of Physics and Technology)

Abstract

In practical engineering and optimization, solving multi-objective optimization (MOO) problems typically involves scalarization methods that convert a multi-objective problem into a single-objective one. While effective, these methods often incur significant computational costs due to iterative calculations and are further complicated by the need for hyperparameter tuning. In this paper, we introduce an extension of the concept of competitive solutions and propose the Scalarization With Competitiveness Method (SWCM) for multi-criteria problems. This method is highly interpretable and eliminates the need for hyperparameter tuning. Additionally, we offer a solution for cases where the objective functions are Lipschitz continuous and can only be computed once, termed Competitiveness Approximation on Lipschitz Functions (CAoLF). This approach is particularly useful when computational resources are limited or re-computation is not feasible. Through computational experiments on the minimum-cost concurrent flow problem, we demonstrate the efficiency and scalability of the proposed method, underscoring its potential for addressing computational challenges in MOO across various applications.

Suggested Citation

  • Ilgam Latypov & Dorn Yuriy, 2025. "$$\gamma $$ γ -Competitiveness," SN Operations Research Forum, Springer, vol. 6(1), pages 1-17, March.
  • Handle: RePEc:spr:snopef:v:6:y:2025:i:1:d:10.1007_s43069-024-00411-y
    DOI: 10.1007/s43069-024-00411-y
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    References listed on IDEAS

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    1. Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Non-Convex Multi-Objective Optimization," Springer Optimization and Its Applications, Springer, number 978-3-319-61007-8, July.
    2. Murat Köksalan & Jyrki Wallenius & Stanley Zionts, 2011. "Multiple Criteria Decision Making:From Early History to the 21st Century," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8042, September.
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