What Is Optimization

Simpson and S.K. Sastry, Chemical and Bioprocess Engineering Fundamental Concepts for First-Year Students, DOI 10.1007/978-l-4614-9126-2 ll, 

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As emphasized earlier in this chapter, this definition of what is optimal does not refer to a Panglossian best of all possible worlds situation. Rather, optimal is to be taken as an adjective that denotes the ubiquitously conserved values for diverse physiological systems that have evolved within the constraints imposed by the sets of molecules and the physical laws governing their behavior on which life as we know it is based. Perhaps what we observe is a best of all compromises situation, which arises from the potentials and constraints afforded by biochemistry. The repeated observation that adaptation by species belonging to each of the three domains of life follows a similar course and employs the same raw material illustrates both the opportunities and constraints faced in adaptation. 

Pomiankowski If one was going to follow the logic that the brain is a sexually selected organ, one would have to argue hypertrophy beyond what is optimal for everyday life. 

To some extent, a disciplinary divide is at work here, as probabilistic models derived from population biology and selection theory differ fundamentally from engineering models, which depend on. .. the surface area of isometric bodies, or the structure of branching networks (McNab, 2002, p. 35). This divide entails differences not only in analytic approach, but also in evaluative criteria that have both polarized the dispute and made it difficult to resolve empirically. However, my point is that these tensions do not require a forced choice between explanatory accounts, which are not intrinsically irreconcilable. Internal constraints may fix the allometric baseline, which selection may modify under certain circumstances. One of the postulates of West and co-workers model is that organisms evolve toward an optimal state in which the energy required for resource distribution is minimized (West and Brown, 2004, p. 38). Toward is the key word here, and the extent to which evolution attains any particular optimality target often reflects compromise with other selective demands physical first principles may constrain what is optimal, but do not always determine what is actual. 

For CFA systems containing sensors the only change will be in the design of the detection cell, since what is optimal for the sensor may not be best for the CFA system. In most cases the detection cell design is a compromise. 

It should be noted that the various ways of canying out the project, and their impact on apparent engineering costs, are not just crafty devices for reducing or increasing engineering costs (although that may be the intention ). The best option may be different on different projects or for different contractors. There is no golden rule as to what is optimal. 

What makes us think that we can imitate enzymes with small molecules I came to the conclusion some time ago that if this is going to be possible - and I frankly think it will be - it will be because nature has optimized the entire system, and what is optimized is a system and not a molecule. It is quite possible that the macromolecules which nature makes are not the only and perhaps even not the best catalysts. But of course when you impose the extra requirement that the genetic information be one-dimensional, this is a tremendous limitation. It is a limitation which makes it certain that you must assemble a polymer which must then spontaneously fold. And if you want to pass on 2-dimensional or 3-dimensional information, the genetic requirements will be so complex that it may be better to make these molecules in order to simplify genetics. So, if it does turn out that we make better catalysts, or at least comparable catalyst enzymes, I think it is just because the whole system has been optimized by nature, whereas we have the option of designing a molecule, and not worrying about how it would reproduce in a self-reproducing way. 

I would like to comment on F. Jacob s remark that biological systems are assembled by tinkering. Tinker mechanisms have an intrinsic flexibility which extensively engineered systems do not have. Biological systems evolve, and what is optimal today is not perfection tomorrow. Perfection does not exist. Tinker mechanisms are probably the cheapest way to solve problems which will change with time. To start from scratch is an expenditure in time and energy which leads to solutions that will be made obsolete by the evolution of the problem to be solved. 

A similar tension may also exist between the Operations Director s short-term objectives and the longer term goals of the company. It is sometimes said that the art of ranning a software house is the art of matching people to projects in an optimal way what is optimal depends, of course, on individuals aspirations and the organization s strategic plans, as well as short-term needs. 

Figure 7.3 presents a flowchart depicting the basic allocation process contained within BS/EN/ISO 11064-1 2001. The process recognizes that some tasks have to be allocated either to a machine or to a human, so to that extent they are mandatory allocations. This leaves a set of preliminary allocations in which the criteria above are more fully engaged in order to decide who (or what) is optimal for undertaking a particular task. This then leaves cases in which both humans and machines could perform the task, meaning that the decision process shifts to one based on who (or what) would be preferable. The basic allocation process, therefore, progresses from who has to do a task to who is best suited and, finally, to who would be preferable. Solutions are based on iteration. The outputs of step 2 are as follows ... 

Define a fitness function that measures the performance of a member (i.e., set of variables) in terms of a single real number. This is now the measure that defines the goal of evolution. In theoretical problems of optimization it is quickly defined. However, in some practical problems there might be some room for interpretation. Consider, for example, optimizing the timetable of an international airplane carrier A number of conflicting concepts of what is optimal have to be discussed and cast into one unified picture. 

Each of the inequality constraints gj(z) multiphed by what is called a Kuhn-Tucker multiplier is added to form the Lagrange function. The necessaiy conditions for optimality, called the Karush-Kuhn-Tucker conditions for inequality-constrained optimization problems, are... 

The gas turbine is a complex system. A typical control system with hierarchic levels of automation is shown in Figure 19-3. The control system at the plant level consists of a D-CS system, which in many new installations is connected to a condition monitoring system and an optimization system. The D-CS system is what is considered to be a plant level system and is connected to the three machine level systems. It can, in some cases, also be connected to functional level systems such as lubrication systems and fuel handling systems. In those cases, it would give a signal of readiness from those systems to the machine level systems. The condition monitoring system... 

What is the optimal flowrate of each separating agent ... 

What is the optimal system configuration (e.g., how should these mass exchangers be arranged Is there any stream splitting and mixing ) ... 

When optimizing industrial ventilation, the real consequences for the environment due to decisions made are of interest. Therefore, the marginal effect on the whole energy system is what is required. This is of course difficult. Many practitioners use electricity produced from coal processes as marginal, but some use natural-gas-fired power plants. It depends mainly on the area and time frame that is being considered. 

The term nonlinear in nonlinear programming does not refer to a material or geometric nonlinearity but instead refers to the nonlinearity in the mathematical optimization problem itself. The first step in the optimization process involves answering questions such as what is the buckling response, what is the vibration response, what is the deflection response, and what is the stress response Requirements usually exist for every one of those response variables. Putting those response characteristics and constraints together leads to an equation set that is inherently nonlinear, irrespective of whether the material properties themselves are linear or nonlinear, and that nonlinear equation set is where the term nonlinear programming comes from. 

Let s consider one rather restricted structural optimization problem, that of a composite laminate. You have seen claimed as attractive advantages of composite structures the fact that we can orient the laminae in a laminate to our heart s content to try to get the most efficient structure. This characteristic is totally unlike what is possible with metal structures. This laminate orientation flexibility is certainly an advantage, but how do we use it ... 

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