Mathematical model of the iterative method of evolutionary coordination of solutions

Roman Mirakhmedov


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.

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