Towards Design of System Hierarchy (research survey)

TL;DR

This survey reviews various approaches and optimization techniques for designing hierarchical and tree-like system structures, including clustering, spanning problems, and network modifications, supported by numerical examples.

Contribution

It provides a comprehensive overview of methods for hierarchical system design, integrating combinatorial optimization and modification strategies, which was lacking in prior surveys.

Findings

Multiple approaches for hierarchical system design are examined.

Optimization problems like spanning trees and network modifications are analyzed.

Numerical examples illustrate the effectiveness of the proposed frameworks.

Abstract

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 procedures, (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 or networks: (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.