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Multicriteria Optimization Problem on Prefractal Graph

Author

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  • Rasul Kochkarov

    (Department of Data Analysis and Machine Learning, Faculty of Information Technology and Big Data Analysis, Financial University under the Government of the Russian Federation, Leningradsky Prospekt 49/2, Moscow 125167, Russia)

Abstract

Even among single-criteria discrete problems, there are NP-hard ones. Multicriteria problems on graphs in many cases become intractable. Currently, priority is given to the study of applied multicriteria problems with specific criteria; there is no classification of criteria according to their type and content. There are few studies with fuzzy criteria, both weight and topological. Little attention is paid to the stability of solutions, and this is necessary when modeling real processes due to their dynamism. It is also necessary to study the behavior of solution sets for various general and individual problems. The theory of multicriteria optimization is a rather young branch of science and requires the development of not only particular methods, but also the construction of a methodological basis. This is also true in terms of discrete graph-theoretic optimization. In this paper, we propose to get acquainted with multicriteria problems for a special class of prefractal graphs. Modeling natural objects or processes using graphs often involves weighting edges with many numbers. The author proposes a general formulation of a multicriteria problem on a multi-weighted prefractal graph; defines three sets of alternatives—Pareto, complete and lexicographic; and proposes a classification of individual problems according to the set of feasible solutions. As an example, we consider an individual problem of placing a multiple center with two types of weight criteria and two types of topological ones. An algorithm with estimates of all criteria of the problem is proposed.

Suggested Citation

  • Rasul Kochkarov, 2022. "Multicriteria Optimization Problem on Prefractal Graph," Mathematics, MDPI, vol. 10(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:930-:d:770878
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    References listed on IDEAS

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    1. F. Liberatore & M. Camacho-Collados, 2016. "A Comparison of Local Search Methods for the Multicriteria Police Districting Problem on Graph," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, March.
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    Cited by:

    1. Rasul Kochkarov & Azret Kochkarov, 2022. "Introduction to the Class of Prefractal Graphs," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    2. Alina Vladimirovna Petukhova & Anna Vladimirovna Kovalenko & Anna Vyacheslavovna Ovsyannikova, 2022. "Algorithm for Optimization of Inverse Problem Modeling in Fuzzy Cognitive Maps," Mathematics, MDPI, vol. 10(19), pages 1-16, September.
    3. Vladimir Sudakov & Alexander Zhukov, 2023. "Fuzzy Domination Graphs in Decision Support Tasks," Mathematics, MDPI, vol. 11(13), pages 1-16, June.

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