Modeling and optimization of adaptive multicomponent systems based on algebraic structures

The paper describes the issues of modeling and optimization of multicomponent systems. The classification of interfaces by types is presented and the corresponding notation is introduced for each of them. A three-dimensional structure is proposed that describes and systematizes operations on the interfaces of the components of the simulated system (integration, conjugation, and filtering), which is an unweighted directed graph that has the properties of an algebraic lattice in each of the three dimensions. For each type of operation, a partial order relation is substantiated on a set of interfaces and an algebraic lattice representation is presented with justification. The proposed structure can be used as an index. With its help, a quick search for the desired interface can be carried out, for optimization of which a depth search algorithm is proposed, which is modified taking into account the design features of the graph. The proposed algorithm has less computational complexity than the classical one, and does not have its main drawbacks - incompleteness and inoptimality when searching with depth restriction. It also shows the application of the proposed approach to the modeling of multicomponent systems based on algebraic structures using the example of a higher education educational program presented as a set of components interacting via standardized interfaces.

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