Hierarchical decomposition

The subgroups were determined based on a hierarchical decomposition strategy for a FCCU (Ramesh et al, 1992). The FCCU was decomposed into four separate units feed.system, catalyst.system, reactor/regenera-tor.system, and separation.system as shown in Fig. 32. Each of these units was further divided into more detailed functional, structural, or behavioral... 

Details of the hierarchical decomposition used to manage the scope of the problem are given in Sravana (1994). There are many considerations in developing a particular decomposition, but the objective is to decompose the process into smaller, more localized malfunction considerations. 

In this way, data interpretation is accomplished by a set of nested numeric-symbolic and symbolic-symbolic interpreters. Note that the hierarchical decomposition results in a distributed set of symbolic-symbolic interpretation problems represented by nodes. Each problem requires intermediate interpretations of numeric data as input to the symbolic-... 

Heuristic based approaches are more relevant for structured products. The most well known heuristic based approach is the hierarchical decomposition method developed by Douglas (Douglas, 1988). In the first level of this method one only looks at the input-output structure of the process. In subsequent levels more detail is added, finally ending with the entire flowsheet. Design decisions are made by using heuristics and short-cut models. An alternative method is due to Siirola (1996) means end analysis. In this method the properties of the feedstock and the desired products are compared. Tasks are defined to eliminate the property differences between the feedstock and the desired product. 

The method we are using is a combination of the hierarchical decomposition (Douglas, 1988) and means end analysis (Siirola, 1996). The three first stages of... 

Formally, a MCDD represents a hierarchical decomposition of a model into constituent entities. Since this decomposition must ultimately terminate, a MCDD should not have directed circuits. Thus, MCDDs are digraphs that have the following properties ... 

Partitioning is most appropriate when one is only interested in the subsets or clusters, while hierarchical decomposition is most applicable when one seeks to show similarity relationships between clusters. Section 2.1 formalizes the combinatorics of the partitional strategy and Section 2.2 does the same for hierarchical methods. The formulations we derive here provide the basis for the application of the simulated annealing algorithm to the underl5dng optimization problem as we show in Section 3. 

Daichendt, M.M., Grossmann, I.E. Integration of hierarchical decomposition and mathematical programming for the sythesis of process flowsheets. Computers Chemical Engineering 22, 147-175 (1998)... 

Solution method refers to the method applied to solve the proposed model e.g. (commercial) standard solvers [standard] (such as CPLEX or CONOPT), a specific optimization method [specific], a hierarchical decomposition approach [decomp.j, or a heuristioal procedure [heur.]. For simulation models, often a finite set of scenarios is evaluated and compared [seen.]. But also genetic algorithms are sometimes used for simulation optimzation [GA]. ... 

We will not elaborate on these here, but the decomposition invites further hierarchical decomposition. 

After partitioning, we have achieved a hierarchical decomposition of the DG in two DGs, the tile graph and the tile, both having a reduced and possibly... 

In the mapping procedure, IDEFO allows ahieiarchi-cal ortop-down decomposition pioachto analyze processes at multiple levels of abstraction (Fulscher Powell, 1999 Kappes, 1997 Plaia Carrie, 1995). The essence of hierarchical decomposition approaches to business process moping, in which a basic, single-activity description of the process is... 

Hierarchical decomposition. This method breaks the design down in such a way that high-level decisions are taken first in the design phase (e.g., identifying reaction—separation train). After the high-level decisions are made, decisions on each unit operation are refined. LinnhofF et al. [43] represented this approach in an onion... 

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