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Searching for Pareto-Optimal Solutions

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Advances in Intelligent Systems and Computing IV (CSIT 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1080))

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Abstract

The problem of narrowing the Pareto set is considered. The existing approaches aimed at solving the problem of finding a set of Pareto optimal solutions has been analyzed. One approach for solving multi-objective problems based on complex using methods for the construction of the Pareto optimal set and evidence theory has been proposed in this paper. The proposed technique allows to evaluate the obtained set of non-dominated alternatives by methods of the evidence theory to find the best (optimal) solution. The proposed approach allows us to obtain a more formalized procedure for narrowing the Pareto set to obtaining a single optimal solution (a single-element Pareto set). The use of the mathematical apparatus of the evidence theory makes it possible to model uncertainty in expert or decision makers judgments (the strict requirement of the “unambiguous” preference of one alternative over the other is removed). Using the proportional conflict redistribution rules for aggregating group expert assessments makes it possible to process expert evidence generated under conflicting, contradiction expert information. Numerical examples of the proposed methodology for integrated application of evidence theory and methods for Pareto set construction to find optimal solutions are given. The results obtained make it possible to improve the quality and effectiveness of finding optimal solutions.

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Acknowledgment

This research was partially supported by the state research project “Development of information and communication decision support technologies for strategic decision-making with multiple criteria and uncertainty for military-civilian use” (research project no. 0117U007144, financed by the Government of Ukraine).

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Authors and Affiliations

  1. Petro Mohyla Black Sea National University, Mykolaiv, Ukraine

    Igor Kovalenko, Yevhen Davydenko & Alyona Shved

Authors
  1. Igor Kovalenko
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  2. Yevhen Davydenko
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  3. Alyona Shved
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Corresponding author

Correspondence to Yevhen Davydenko .

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Editors and Affiliations

  1. Department of Artificial Intelligence, Lviv Polytechnic National University, Lviv, Ukraine

    Natalya Shakhovska

  2. Institute of Computer Science and Information Technologies, Lviv Polytechnic National University, Lviv, Ukraine

    Mykola O. Medykovskyy

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Kovalenko, I., Davydenko, Y., Shved, A. (2020). Searching for Pareto-Optimal Solutions. In: Shakhovska, N., Medykovskyy, M.O. (eds) Advances in Intelligent Systems and Computing IV. CSIT 2019. Advances in Intelligent Systems and Computing, vol 1080. Springer, Cham. https://doi.org/10.1007/978-3-030-33695-0_10

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