Towards Design of System Hierarchy (research survey)

The paper addresses design/building frameworks for some kinds of tree-like and hierarchical structures of systems. The following approaches are examined: (1) expert-based procedure, (2) hierarchical clustering; (3) spanning problems (e.g., minimum spanning tree, minimum Steiner tree, maximum leaf spanning tree problem; (4) design of organizational " optimal " hierarchies; (5) design of multi-layer (e.g., three-layer) k-connected network; (6) modification of hierarchies: (i) modification of tree via condensing of neighbor nodes, (ii) hotlink assignment, (iii) transformation of tree into Steiner tree, (iv) restructuring as modification of an initial structural solution into a solution that is the most close to a goal solution while taking into account a cost of the modification. Combinatorial optimization problems are considered as basic ones (e.g., classification, knapsack problem, multiple choice problem, assignment problem). Some numerical examples illustrate the suggested problems and solving frameworks.