Problem-solving techniques network method

Combinatorial. Combinatorial methods express the synthesis problem as a traditional optimization problem which can only be solved using powerful techniques that have been known for some time. These may use total network cost direcdy as an objective function but do not exploit the special characteristics of heat-exchange networks in obtaining a solution. Much of the early work in heat-exchange network synthesis was based on exhaustive search or combinatorial development of networks. This work has not proven useful because for only a typical ten-process-stream example problem the alternative sets of feasible matches are cal.55 x 10 without stream spHtting. 

Publications on optimal design of tree networks are further divided into single-branch trees or pipelines (C6, F4, L3, L6, S8) and many-branch trees (B7, C7, F4, Kl, K2, M3, M9, Nl, R5, W10, Y1, Zl). For our purposes, since the pipeline problems can always be solved using the optimization methods developed for the many-branch tree networks, we need to dwell no further on this special case. On the other hand, it is important to note that the form of the objective function could influence the applicability of a given optimization method. For the sake of concreteness, problem formulations and optimization techniques will be discussed in the context of applications. 

The IDEAS approach is a reactor superstructure method that represents all reactor networks as the combination of two generalized blocks. When the system is viewed in this manner, the resulting equations describing the problem can be made linear. An advantage of this is that traditionally nonlinear reactor network problems may then be solved via an LP technique, such as that described by the LP formulations in Section 8.6.1. And as a result, the solution to the linear system is guaranteed to be globally optimal. 

The high degree of complexity of typical real problems implies that the final method used to solve a problem is more often a combination of several methods, such as soft computing techniques (namely, fuzzy logic, genetic algorithms, and neural networks) with more classic ones (such as algebraic, analytical, numerical, and stochastic methods). 

The neural network approach is an alternative way of solving the problem. Unlike multiple linear or nonlinear regression techniques, which require a predefined empirical form, the neural network can identify and learn the correlative patterns between the input and the corresponding output values once a training set is provided. This approach avoids some of the shortcomings encountered in more traditional correlative methods, and with modem software it can provide useful models in a relatively short time for both linear and non-linear systems. 

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