This monograph summarizes the materials of foreign and Russian scientists and the results of the authors' research in these areas. A triune approach to the construction of artificial intelligent hierarchical systems is presented, based on modern research in such fields of artificial science as homeostatics, synergetics and evolutionary modeling. Methods of constructing hierarchical artificial intelligent systems for solving optimization decision-making problems on graphs are described. Algorithms of analysis and synthesis of optimization decision-making problems on graphs are considered.