Global criteria

The optimization results for different criteria may be conflicting in the sense that they show optima at different values of the factors. One does not need to find the optimum of the two (or more) responses separately, but rather an adequate compromise. There are several ways of doing this. The most usual, but not necessarily the best is to combine (elemental) criteria in some way to obtain what have been called global criteria. Again several such criteria have been propo.sed. for instance the COF (chromatographic optimization function) 5] given by ... 

Spectral analysis shows quite clearly that the various types of atoms are exactly the same on Earth as in the sky, in my own hand or in the hand of Orion. Stars are material objects, in the baryonic sense of the term. All astrophysical objects, apart from a noteworthy fraction of the dark-matter haloes, all stars and gaseous clouds are undoubtedly composed of atoms. However, the relative proportions of these atoms vary from one place to another. The term abundance is traditionally used to describe the quantity of a particular element relative to the quantity of hydrogen. Apart from this purely astronomical definition, the global criterion of metallicity has been defined with a view to chemical differentiation of various media. Astronomers abuse the term metaT by applying it to all elements heavier than helium. They reserve the letter Z for the mass fraction of elements above helium in a given sample, i.e. the percentage of metals by mass contained in 1 g of the matter under consideration. (Note that the same symbol is used for the atomic number, i.e. the number of protons in the nucleus. The context should distinguish which is intended.)... 

Use Theorem 5.2.1 to compute the number of interior vertices and faces. If they are negative or non-integer, then the (r, 3)-boundaiy is non-extensible. This is a global criterion. 

Resolution, like the separation factor, differs for each specific component pair and therefore fails as a global criterion of separation. For analytical separations, more universal criteria have evolved, such as plate height, number of plates, rate of generation of plates, and peak capacity (Chapter 5). While these indices differ somewhat from one component to another, they effectively establish a ballpark figure of merit for different systems and different conditions of operation. 

The quality of the eventually selected separation depends on the appropriateness of the criterion and it is therefore important to select the criterion well. This selection consists of several steps. The first is to select what is called an elemental criterion. which describes the separation quality of two substances, the second is to derive from the elemental criterion value a global criterion. There are two types of elemental criteria. They have been called p- and. v-criteria. The p criteria compare in some way the height of the peaks with the valley in between them. Several variants have been proposed. Two of them are shown in Fig. 6.3 (the valley-to-peak ratio F, . = 1 — v/hi and the... 

No Preference Methods (e.g., global criterion and neutral compromise solution) These methods, as the name indicates, do not require any inputs from the decision maker either before, during or after solving the problem. Global criterion method can find a Pareto-optimal solution, close to the ideal objective vector. 

Under APS, planning, with its synchronization emphasis, dominates and sequencing (or scheduling) is subservient to it. The operations to manufacture a part are initiedly placed in the plan to support a global criterion, say customer order due date, tmd then the sequencing of these operations is done to adhere to the plan as closely as possible. 

Method of global criterion (Hwang and Masud, 1979) and compromise programming (Zeleny, 1982) fall under the class of MCMP methods that do not require any preference information from the DM. 

Let the ideal values of the objectives/i,/2,...,/ji be /, f, ---, fi- The method of global criterion finds an efficient solution at is "closest" to the ideal solution in terms of the distance metric. It also uses the ideal values to normalize the objective functions. Thus the MCMP reduces to... 

Compromise Programming is similar in concept to the method of global criterion. It finds an efficient solution by minimizing the weighted distance metric from the ideal point as given next ... 

There are many techniques for solving MOMP—compromise programming, the weighted average method, and global criterion and GP methods, to name a few. GP techniques are used in this chapter because they measure... 

Note The segmentation operation yields a near-optimal estimate x that may be used as initialization point for an optimization algoritlim that has to find out the global minimum of the criterion /(.). Because of its nonlinear nature, we prefer to minimize it by using a stochastic optimization algorithm (a version of the Simulated Annealing algorithm [3]). 

This criterion resumes all the a priori knowledge that we are able to convey concerning the physical aspect of the flawed region. Unfortunately, neither the weak membrane model (U2 (f)) nor the Beta law Ui (f)) energies are convex functions. Consequently, we need to implement a global optimization technique to reach the solution. Simulated annealing (SA) cannot be used here because it leads to a prohibitive cost for calculations [9]. We have adopted a continuation method like the GNC [2]. 

But for power station applications, the thermal efficiency is not the only measure of the performance of a plant. While a new type of plant may involve some reduction in running costs due to improved thermal efficiency, it may also involve additional capital costs. The cost of electricity produced is the crucial criterion within the overall economics, and this depends not only on the thermal efficiency and capital costs, but also on the price of fuel, operational and maintenance costs, and the taxes imposed. Yet another factor, which has recently become important, is the production by gas turbine plants of greenhouse gases (mainly carbon dioxide) which contribute to global warming. Many countries are now considering the imposition of a special tax on the amount of CO2 produced by a power plant, and this may adversely affect the economics. So consideration of a new plant in future will involve not only the factors listed above but also the amount of CO2 produced per unit of electricity together with the extra taxes that may have to be paid. 

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