Multi-objective decision systems for the management, monitoring and control of complex processes require the application of new methods and models of abstraction and formal description based on intelligent computing structures to ensure optimal overall decision-making. These computing structures can be built on the basis of Multi-Agent systems. In this paper it is proposed the development of a Multi-Objective Based Multi-Agent Decision-Making System that ensures the process of searching for the optimal solution based on genetic algorithms and its application in the decision-making process. The Multi-Agent system features a distributed computing structure consisting of lots of heterogeneous data processing nodes. The functionality of agents is described based on mathematical models and sequence diagram, which explains the interaction between the set of Agents. The structure of the decision-making system is presented on two levels of abstraction: the Multi-Agent level of production and management, and the Information level of communication, storage and data processing.