Hierarchical Overlapping Coordination for Large Scale Systems

Abstract

The basic hierarchical overlapping coordination method is briefly reviewed. Three generalizations to this method with respect to convergence, problem formulation, and multiple objectives are presented. It is explained how a potential convergence problem in the basic scheme can be overcome by additional optimizations with respect to some interaction variables. In the problem formulation extension, the different decompositions are allowed to have different variables. Classical hierarchical methods are used for the overlapping coordination scheme resulting in a three-level structure. The single-objective hierarchical overlapping scheme is extended to multiple objectives using the Surrogate Worth Trade-off (SWT) method. Overlapping coordination and the Dantzig-Wolfe algorithm are compared. A simple example is used to articulate the respective attributes. Finally, the concept of hierarchical holographic modeling, obtained as an extension of the concept of hierarchical overlapping coordination, is presented with some preliminary mathematical results and illuminating examples.