Problem decomposition

For linear models, the Q-R factorization can be successfully applied for both problem decomposition and estimation purposes. In contrast, nonlinear models require the selection of an appropriate technique that can manage the complexity of the nonlinear constraints in a reasonably low run time. 

The pinch decomposition is very useful in heat exchanger network design, as it decomposes the problem into two smaller problems. It also indicates the region where heat transfer matches are most constrained, at or near the pinch. When multiple hot or cold utilities are used, there may be other pinches, termed utility pinches, that cause further problem decomposition. Problem decomposition can be exploited in algorithms for automatic heat exchanger network synthesis. 

We use an Artificial Intelligence technique called the Problem Decomposition Strategy (14, 15) to tackle this problem. We divide the problem of computing a quantity into a number of sub-problems, each involving the computation of a formula with several sub-quantities. When more than one formula is applicable, they are tried one by one. The entire problem space can be represented as an AND/OR tree, and a Depth-first Recursive Search is employed to traverse the tree. The leaf nodes represent quantities whose values are known. The search terminates at the leaf nodes and returns the value to the level above. When a dead-end is reached, the system progressively backtracks to the levels above in an attempt to select smother formula. If the complete search space is exhausted, the system reports that the problem is unsolvable and prompts the user for more information. 

The theoretical yield of a reaction is the calculated amount of product that should be obtained in a reaction. But in practice, something less than the theoretical yield, the actual yield, is obtained. For many reasons—impure reagents, solubility problems, decomposition, or spillage—the amount of product isolated from a reaction is frequently less than that calculated from the balanced equation. The fraction of the theoretical yield actually obtained in a reaction is expressed as the percent yield of the reaction. 

Energy utilization only becomes possible as a result of increasing the column pressure, and this means higher investment costs and may result in material problems (decomposition, side reactions, etc.). 

A multidisciplinary community or project is made up of people from more than one discipline that come together as equal stakeholders to work on complex problems that cannot be solved by a single disciplinary community alone. If the complex problem can be broken down into a set of problems that each discipline can solve separately and then reintegrate to solve the whole, multidisciplinary teams can be very efficient at repeatedly solving versions of the challenge. A multidisciplinary person is a person with the knowledge to be a member of more than one disciplinary community. Multidisciplinary teams must deal primarily with problem decomposition and solution recomposition problems in addition to the knowledge application problem. 

Problem decomposition reduces complexity and memory requirements and the granularity of the processes is really important as analyze in Section 4.2. We must reduce the complexity enough to be able to run sub-problems singularly. The more partitions are produced, the easier the overall process can be divided among N processors but beyond a certain point the decomposition strategy becomes inefficient as the degree of overlapping increases to much. 

Description i) a master sub-problem decomposition approach selects integer variables i.e. number of trays) in a master program and ii) an optimal column design is... 

Wahnschafft, O. M., Le ReduUer, Westerberg, A. W. (1993). A Problem Decomposition Approach for the Synthesis of Complex Separation Processes with Recycles. Ind. Eng. Chem. Res., 32,1121-1140. 

Problem decomposition. It comprises the individuation of the goal (i.e. the decisional problem to be solved), of the criteria/sub-criteria on the base of which evaluating alternatives, and of the alternatives to be ranked in respect to the goal, eventually to select the best one. 

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