Mathematical model of the iterative method of evolutionary coordination of solutions

Roman Mirakhmedov

Abstract


The shortcomings of existing methods for making decisions by groups of experts are discussed and a conclusion is drawn in favor of the method of evolutionary coordination of decisions. The principles on which this method is based are given, along with definitions, terminology and procedures. The formulation of the problem, the limiting and initial values of the initial quantities are given. A mathematical model of the iterative method of evolutionary coordination of solutions has been constructed. The results of a theoretical consideration of the method of evolutionary coordination of decisions by a group of actors are presented. The dependences of the probabilities of correct and incorrect solutions of local problems on the creative characteristics of the actors, on the difficulties of the problems, on the number of actors and on the number of iterations were found. The method is based on the provisions of the theory of metasystem transitions by V. Turchin using the rules of interaction between actors. The rules are formulated on the basis of this theory in accordance with the operators of genetic algorithms, which act as a coordinator in the process of work of a group of actors. At the stages of generating solutions and their examination, ternary logic is used. Actors in the process of group work can give correct answers, erroneous answers and “I don’t know” answers. To construct a mathematical model, the principles of probability theory, the one-parameter Rasch model modified for the new method, and Condorcet's jury theorem were used. A comparison was made of the results of using the mathematical model and computer calculations using the Monte Carlo method. Conclusions are drawn about the predictive capabilities of the proposed model.

Full Text:

PDF (Russian)

References


Popov B.M. Metaphysics of nature-like technologies. ‒ Voronezh:

Kvarta. ‒2019. ‒ 60 p.

Alexandros Tzanetos, Iztok Fister Jr., Georgios Dounias. A comprehensive database of Nature-Inspired Algorithms // Data in Brief. Volume 31. 2020. P. 2–9. https://doi.org/10.1016/j.dib.2020.105792

Tkachenko Yu. L. What technologies are nature-like? A new topic for conceptual discussion // Advances in modern science. – 2016. –№3, Vol. 1. P.101–107

Yegorova-Gudkova Т. Management that resemble natural ones and design of self-organizing economic systems//International scientific journal "Science. Business. Society". – 2018. –Vol. 3, Issue 2. –P. 75-77.

A.A. Zhdanov. General systems theory: analysis and additions. Electronic edition. M.: Publishing house "Laboratory of Knowledge". – 2024 – 192 p.

Karpov V.E. Methodological problems of evolutionary computing // Artificial intelligence and decision making. – 2012. – No. 4. – pp. 95-102.

Fields, Chris, James F. Glazebrook, and Michael Levin.. Principled Limitations on Self-Representation for Generic Physical Systems // Entropy. –2024. Vol. 3. P. 1–16.

V.I. Protasov. Methodology and practice of building collective intelligence systems. Dissertation for the degree of Doctor of Technical Sciences. –Nizhny Novgorod, NSTU named after. Alekseeva. –2021. –314 p,

L.V. Markaryan. Models and algorithms of collective intelligence systems. – M: Ed. MISiS. – 2020. – 104 p.

Markaryan L.V. Analysis and optimization of the decision-making process based on the method of evolutionary coordination of decisions // Mining information and analytical bulletin (scientific and technical journal). –2013, No. 9. P. 301-306.

] Protasov V.I., Mirakhmedov R.O., Potapova Z.E., Sharnin M.M., Sharonov A.V. Reducing errors of the first type when recognizing the contours of aircraft using the collective intelligence of UAVs // News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences. –2018, No. 6-3 (86). –C. 70-82.

Protasov, Z.E. Potapova. Methodology for radically reducing the likelihood of making erroneous decisions in collective intelligence systems // International scientific journal “Modern information technologies and IT education”. –2019, volume 15, no. 3. – pp. 588 – 601.

R. Mirakhmedov, Z. Potapova, V. Protasov . MESING – a new method of organizing the joint work of neural networks and its metrology // Journal of Physics: Conference Series, 2021, v. 1727, 012004. DOI 10.1088/1742-6596/1727/1/012004.

Protasov V.I. Collective intelligence systems. Theory and practice. – M: University book. – 2024. – 230 p

Turchin, V.F. Phenomenon of science. Cybernetic approach to evolution. -M.: Sinteg, 1993. — 456 p.

Rasch G. Probabilistic Models for Some Intelligence and Attainment Tests // Expanded Edition, with Foreword and Afterword by B.D. Wright. Chicago: University of Chicago Press,1980.

Condorcet, marquis de (Marie-Jean-Antoine-Nicolas de Caritat) (1785), Essai sur l’application de l’analyse à la probabilité des décisionsrendues à la pluralité des voix. Imprimerie Royale, Paris.

Holland, J.H. Adaptation in natural and artificial systems. –University of Michigan Press, Ann Arbor, 1975. —228 p.

Y. Koriyama. A resurrection of the Condorcet Jury Theorem Balázs Szentes // Theoretical Economics. 2009, v.4. — P. 227–252.

V. Protasov. Mathematical model of the method of evolutionary coordination of decisions // News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences. – 2012, No. 2 (46). – P. 29-37.


Refbacks

  • There are currently no refbacks.


Abava  Кибербезопасность IT Congress 2024

ISSN: 2307-8162