Constructing economic and mathematical models of multicriteria optimization based on hybrid metaheuristics

Many problems requiring finding optimal solutions may arise in the process of building and managing socio-economic systems. The use of traditional methods of deterministic search is limited by the presence of nonlinear relationships between elements, conflicting interests of agents, hard and soft constraints, and uncontrollable environmental factors. For such problems, it is recommended to use stochastic methods that take into account the random nature of variables in the objective functions and constraints, which are capable of finding acceptable solutions in an acceptable time even under conditions of information uncertainty. In recent years, population metaheuristics, which simultaneously explore several solutions, have undergone significant development. Interest in these methods is due to their suitability for non-convex solution spaces, the absence of conditions on the type of the objective function, the ability to take into account hard and soft constraints, and high convergence. However, according to the no free lunch theorem, there is no metaheuristic that can solve all optimization problems. The article shows that the choice of a specific algorithm is based on the conceptual and mathematical formulation of the optimization problem and the specifics of the implementation of search operations. Despite their subject independence and high flexibility, in practice such algorithms do not provide acceptable results when used in their canonical form. In such situations, they should be modified to suit the specifics of the problem being solved. The article proposes to take into account uncertainty (incompleteness, inaccuracy, unreliability, ambiguity of incoming data) by hybridizing the selected metaheuristics with different methods of fuzzy logic used for identification, evaluation and aggregation of information NON-factors. The article also formulates recommendations for choosing an approach to reducing the set of optimization criteria for the case of multi-objective problems. The use of hybrid algorithms built on the basis of fuzzy logic and swarm intelligence methods will improve the stability and achieve the adequacy of optimization models.