Optimization principles

Optimization pervades the fields of science, engineering, and business. In physics, many different optimal principles have been enunciated, describing natural phenomena in the fields of optics and classical mechanics. The field of statistics treats various principles termed maximum likelihood, minimum loss, and least squares, and business makes use of maximum profit, minimum cost, maximum use of resources, minimum effort, in its efforts to increase profits. A typical engineering problem can be posed as follows A process can be represented by some equations or perhaps solely by experimental data. You have a single performance criterion in mind such as minimum cost. The goal of optimization is to find the values of the variables in the process that yield the best value of the performance criterion. A trade-off usually exists between capital and operating costs. The described factors—process or model and the performance criterion—constitute the optimization problem. ... 

Let us illustrate the above important optimization principle by suggesting how to best operate various combinations of mixed flow reactors for a fermentation which follows Monod kinetics, and where... 

Yann, C., Siarry, P. (eds.) (2004) Multiobjective Optimization Principles and Case Studies., Springer, Berlin, Germany. 

Given the density of Chi in PSI, it is immediately obvious that any detailed description of energy transfer in this system will need to handle both weakly coupled (Forster-type) and strongly coupled (excitonic) systems self consistently. It is also evident that discerning rate limiting steps and optimizing principles may not be straightforward. 

When applied to a system with a large number of elements, the distributions are measured by thermodynamic probability (W) the most probable distribution is such that IV is a maximum. This optimal principle is consistent with tile condition of maximum entropy (5) cited... 

In summary, we see that the study of nonequilibrium systems gives us some understanding of the process of evolution. The appearance of a certain type of organization or order is through fluctuations and kinematic considerations. In general we cannot associate a strict optimization principle to evolution there is no strict Darwinian selection of the fittest. 

In the literature, some computer models describing the evolution of copolymer sequences have been proposed [26,28]. Most of them are based on a stochastic Monte Carlo optimization principle (Metropolis scheme) and aimed at the problems of protein physics. Such optimization algorithms start with arbitrary sequences and proceed by making random substitutions biased to minimize relative potential energy of the initial sequence and/or to maximize the folding rate of the target structure. 

Werner J. H., Kolodinski S. and Queisser H. J. (1994), Novel optimization principles and efficiency limits for semiconductor solar cells , Phys. Rev. Lett. 72, 3851-3854. 

Let us consider the data set of Figure 2.19 to explain the Pareto-optimality principle. Suppose 12 experiments are performed and two responses (yi and y2) are measured for each experiment. Suppose the first response corresponds to resolution, and the second to migration time. The first response thus should be maximized, while the second minimized. The line connecting the experiments 1, 2, and 7 links the Pareto-optimal points for this situation. When comparing, for instance, experiments 1 and 4, experiment 1 is considered Pareto-optimal because it dominates. Similarly, experiment 2 dominates experiment 6. In both cases, migration time is shorter for a similar resolution. 

OPTIMA Library, 2564-2565 Optimality, principle of, 1726-1727 Optimal solution, 2528, 2536 Optimal value (of linear program), 2528 Optimization ... 

Poon, C.-S. 1983a. Optimal control of ventilation in hypoxia, hypercapnia and exercise. In B.J. Whipp and D.M. Wiberg (Eds.), Modelling and Control of Breathing, pp. 189-196, New York, Elsevier. Poon, C.-S. 1983b. Optimality principle in respiratory control. Proceedings of die Second American Control Conference, pp. 36-40. 

Chao, E.Y. and Rim, K., Application of optimization principles in determining the applied moments in human leg joints during gait, J. Biomech., 6,497,1973. 

Agarwal, G.C. and Logsdon, J.B. 1990. Optimal principles for skilled hmb movements and speed accuracy tradeoff. Proc. Ann. Int. Conf. IEEE Eng. Med. Biol. Soc. 12 2318 2319. 

Great efforts have been undertaken to describe the intricate geometry of river networks [363]. In Chap. 6 we illustrated some models, such as the Peano network, which resembles fractal river basins. Another well-known structure that was proposed to describe better the evolution and formation of river basins and that agrees with most of the observations is the Optimal Channels Network (OCN) model, based on some optimization principles that minimize the energy expenditure by the net-... 

A.25. Organizational structure for radiation protection. The structure of the organization responsible for the implementation of the radiation protection programme, the procedures necessary for implementation of the programme, the effectiveness of the management and its commitment with respect to radiation protection, including apphcation of the optimization principle, should aU be assessed... 

The total sample sets were separated into calibration set and validation set. Cross validation was first used in calibration sample set to find the optimal principle component number. From figure 4 we can see the best principle component nmnber to be 10 with corresponding highest Rev of 0.91 and lowest RMSEcv of 0.41. Model accuracy was then evaluated on the validation set using the root mean square error of prediction (RMSEP), correlation... 

Nei, M., Kumar, S., and Takahashi, K., The optimization principle in phylogenetic analysis tends to give incorrect topologies when the number of nucleotides or amino acids used is small, Proc. Natl. Acad. Sci. Washington, 95, 12390-12397, 1998. 

Radiation sources and installations should be provided with the best available protection and safety measures under the prevailing circumstances, so that the magnitudes and likelihood of exposures and the number of individuals exposed be as low as reasonably achievable, economic and social factors being taken into account, and the doses they deliver and the risks they entail be constrained (optimization principle or ALARA -as low as reasonably achievable). 

Kapur J.N. Kesavan H.K. 1992. Entropy Optimization Principles with Applications. San Diego Academic Press. 

When dealing with large-quantity production of a selected material, it is worthwhile to invest a substantial effort in mathematical modeling of the non-linear chromatographic process.In contrast, when preparing small amounts of material, optimization principles can be applied qualitatively since time becomes the most crucial parameter for the delivery of the pure compounds for the initial testing. Economic aspects are less critical for laboratory scale PHPLC compare to production scale purifications. 

Design and optimization principles of biogas reactors in large scale applications... 

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