OPTIMAL DECOMPOSITION OF LARGE-SCALE SYSTEMS


Tiit Riismaa and Otu Vaarmann, Institute of Cybernetics at Tallinn Technical University, Tallinn 12618, Estonia, Phone: +372 6204192 Fax: +372 6204151
tiitr@ioc.ee vaarmann@ioc.ee


ABSTRACT: A method of description and optimization of the structure of multi-level decision-making system is presented. The set of feasible structures for such class of systems is defined and the representation of this set is constructed. A new graph theory based method for presentation of feasible set of structures is also given. This relation enables to determine the process of creation and cancellation of levels and change the number of levels of hierarchy. It is shown that the given choice of variable parameters and the statement of the optimization problem as a double minimum problem enable to construct methods for finding a global optimum of objective function and select the corresponding hierarchical structure. Two finite step numerical algorithms are constructed – algorithm of local search and recursive algorithm. The approach is given in basic terms of graph theory, convex analysis and integer programming. For finding proper values for coordination parameters for problems in convex programming some rapidly convergent iterative methods are developed, their convergence properties and computational aspects are examined. Problems of their global implementation and polyalgorithmic approaches are discussed as well.


KEYWORDS: Large-scale systems, multi-level decomposition, hierarchical structure, structure optimization, decomposition-coordination schemes, polyalgorithmic strategy, graph theory, mathematical programming, integer programming, nonlinear equations.

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