Математические и графовые модели специализированных мультиагентных систем с распределенным решением прикладных задач

Abstract

The concept of a specialized multi-agent system (SMAS) as a system designed for a distributed solution of either one applied problem or a highly limited range of applied problems is considered. Such problems frequently require a large number of homogeneous operations, which can lead to a significant increase in the size of the system and, as a result, to inefficient control and a drop in performance. Therefore, it is advisable to divide a large-sized open SMAS into classes of agents and find relationships between them. This corresponds to dividing the applied task T into subtasks and determining relations between these subtasks. Such a path entails a two-level distributed control over SMAS agents. At the first and second levels, respectively, the relations of agents within classes and between classes of agents are studied. This paper proposes a multi-model approach to constructing, modeling, and analyzing SMAS. The properties of the agent and its mathematical model, described by a 5-digit set, as well as the mathematical model of the class of agents, described by a 12-digit set, which includes such components as the collective knowledge base of agents, the collective communication environment, mental, social, and other components, are discussed. Relations between classes of agents are reflected in a mathematical model of open SMAS. If a partition of a problem T is represented by an undirected acyclic graph GR′ whose terminal vertices have degree one and whose interior vertices have degree two, then GR′ is defined as a simple tree. In the case when any class of agents is a complete graph К then the Cartesian product CP′ = GR′ × Kn, according to the proved theorem, is a graph model of an open SMAS, consisting of the components К and connectives between them. According to the corollary of this theorem, it is possible to pass from CP′ to the multigraph model MYL′ = (MV′, ME′) of the system, if the components К are associated with the vertices of this model mv′ com  MV′, and the connectives are associated with its edges me′ con1  ME′. Moreover, the number of edges between any two vertices MYL′ is equal to n. The analysis of multigraph models of open SMAS of large sizes will significantly reduce the complexity of their study at the structural level.