Essential Features of Optimization Problems

Essential Features of Optimization Problems The solution of optimization problems involves the use of various tools of mathematics, which is discussed in detail in Sec. 3. The formulation of an optimization problem requires the use of mathematical expressions. From a practical viewpoint, it is important to mesh properly the problem statement with the anticipated solution technique. Every optimization problem contains three essential categories  

An objective function to be optimized (revenue function, cost function, etc.) 

Categories 2 and 3 comprise the model of the process or equipment category 1 is sometimes called the economic model. 

TABLE 8-6 Six Steps Used to Solve Optimization Problems 

1 Analyze the process itself so that the process variables and specific characteristics of interest are defined (i.e., make a list of all the variables). 

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Thus, methods are now becoming available such that process systems can be designed to manufacture crystal products of desired chemical and physical properties and characteristics under optimal conditions. In this chapter, the essential features of methods for the analysis of particulate crystal formation and subsequent solid-liquid separation operations discussed in Chapters 3 and 4 will be recapitulated. The interaction between crystallization and downstream processing will be illustrated by practical examples and problems highlighted. Procedures for industrial crystallization process analysis, synthesis and optimization will then be considered and aspects of process simulation, control and sustainable manufacture reviewed. 

During recent years, the problem of optimization of separation techniques in thin-layer chromatography has been tackled in both theoretical treatments (129-133) and in the development of instrumentation (134-136). In overpressured TLC (137) a pressurized ultramicrocham r is used. The essential feature of this chamber system is that, in contrast to the rigid glass plate used in the earlier ultramicrochamber (138,139), the sorbent layer is completely covered by an elastic membrane under external pressure, so that vapor phase above the layer is eliminated. Solvent is admitted into the chamber under overpressure by means of a pump system. This technique essentially combines the... 

Independent of the exact features of the model or criterion defining the protein s folded state, the computational demands of evaluating thermodynamic and kinetic properties of these models can be formidable. At the present time, the best methods combined with the most powerful computational engines are inadequate to fold an all-atom model of a protein in computo. As such, a careful choice of the computational method is essential. The development of new computational methods is infinite in its possibilities. The field of development of conformational optimization algorithms for proteins has shown rapid progress in recent years. This rapid development of new algorithms promises to continue. This article provides a snapshot of the field of protein structure prediction as a problem of conformational optimization. There is an emphasis on the most general and fundamental methods where further development appears to be most likely. The discussion is not intended to be a comprehensive review or even a survey of the most effective methods. The reader is referred to the references for a more comprehensive discussion. 

This first step is obvious but often overlooked simply know the material. Table I provides a systematic overview of the important properties and specific information which should be known before one embarks upon the synthesis of a particular material. The requirement for detailed knowledge of the chemical, physical, colloidal, electronic and optical properties of the materials involved is often ignored at the outset of a synthesis. In the eventuality that there is no need to produce particles of controlled size and morphology, there is little need for an appreciation of all the critical properties of a material. However, for those applications which require particles with specific characteristics, it is essential to understand as much about the material as possible to optimize the opportunity for discrete control of particle features, as well as to ensure that problems such as poor yield from a particular precursor or irreversible agglomeration are avoided or minimized. 

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