Criterion for optimization

Determine the criterion for optimization and specify the objective function in terms of the above variables together with coefficients. This step provides the performance model (sometimes called the economic model when appropriate). 

Figure 5.4-38. Criterion for optimization as a function of run number (reprinted from Marchal-Brassely et al. (1992), Optimal operation of a semi-batch reactor by self-adaptive models for temperature and feed profiles . Copyright (1992), with permission from Elsevier Science).

The criterion for optimal design is the same as that for single-product campaigns. The horizon constraint (7.4-34) is reformulated in that the cycle times are defined differently. Assuming UIS policy, this constraint for mixed-product campaigns is given by ... 

Let us next consider the two other cases of Fig. 19.3. For irreversible exothermic reactions the criterion for optimal operations has also been presented by Konoki (1956b). For endothermic reactions the optimal criterion has yet to be developed. In all these cases a trial-and-error search keeping far from the regions of low rates is recommended. 

Konoki (1961) presents the criterion for optimal operations however, in preliminary design a few good guesses will suffice to closely approach optimal operations. 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

For a reactor operating with constant output, the criterion for optimal performance is for the cooling medium to have the highest possible temperature in the heat removal system. For a working example of the nonadiabatic reactor, there are 4631 cylindrical tubes with inner diameters of 7 mm packed with a catalyst and surrounded by a constantly boiling liquid at 703 K. Sulfur dioxide and air are fed into the reactor at a total pressure PT, in volume fractions of > s,, 2 =0.11 and >v,2 =0.10. The empirical expression oftakes into account diffusion and reaction kinetics, and we have... 

In this example, a series of cumulative extractions at increasing density (at a constant temperature) was carried out initially. Then when the optimum density (0.81 g/mL) was selected - with optimum determined by the fastest time to constant weight loss, the temperature was systematically varied. This yielded the information that a temperature of 80 C and a density of 0.81 g/mL would provide an initial optimal set of conditions again the criterion for optimal was the fastest time to constant weight loss from the sample. Then an extensive set of statistically chosen parameters was selected to further... 

The criterion for optimization is the objective function and not, for example, its derivative. 

However, given that various psychophysiological studies have shown detrimental effects of very short SRT s, the general reconunendation "faster is better" (c the title of Smith, 1983) does not seem to be appropriate for HCI, except for programmers (Lambert, 1984). Therefore, the reconunendation is to determine an optimal SRT for the task in question by means of a psychophysiological study. The criterion for optimal would be no marked increases in cardiovascular... 

Sharma, S. and Rangaiah, G.R (2013b) An improved multi-objective differential evolution with a termination criterion for optimizing chemical processes. Computers Chemical Engineering, 56, 155-173. 

The primary objective of this paper is to present a conceptually clear derivation of discounted cost criterion for optimizing the maintenance of systems subject to stochastic cinnulative damage. The model considers a periodic inspection pohcy and aims to optimize the inspection interval as well as the degradation level that would trigger a preventive maintenance of the system. The proposed derivation is general and it can be reduced to special cases of homogeneous or nonho-mogeneous Poisson processes, or renewal processes. 

Previous studies mostly adopted asymptotic cost rate criterion for optimizing maintenance policies. However, the optimization of discounted cost is more pertinent to practical apphcations. Our experience also suggests that practical applications of compound point processes are limited due to lack of clarity about the mathematical derivations of cost rate and life expectancy. 

The energy ( ) is of central importance in variational electronic structure methods as a criterion for optimizing... 

A general criterion for optimizing the metal CMP process is the controlled regulation of material removal, while simultaneously securing the processed surface from various CMP-related defects like scratches, dishing, delamination, erosion, contamination, line deformation, and galvanic corrosion (Baneijee and Rhoades, 2008 Choi and Korach, 2009). The considerations for improving material removal rates (MRRs) are mostiy relevant in the context of bulk Cu CMP, but are relatively less critical for the thin (<5 nm) diffusion barrier metal films. However, the requirement for defect control continues to remain a major issue in essentially all cases of metal CMP (Chandrasekaran et al., 2004). 

After presenting the relevant theoretical details, concept of and their relationship to solid surface free energy, it is now appropriate to examine the various surface chemical conditions which predict optimum adhesion. Thermodynamic work of adhesion, W, is the commonly used criterion for optimizing adhesion, but, as will be discussed in the following paragraphs, there are other quantities which should also be considered. 

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