Generic Problem Formulations

It is important to note that if generic problem formulations are to be used, it is especially important that they are developed very carefully in the first place, that their domains of applicability are carefully defined, and that users should doublecheck on every occasion that they are fully appropriate to the case in hand or adjust them as necessary. 

Take advantage of opportunities to devise generic problem formulations, but check their appropriateness for each individual assessment. 

The use of uncertainty analysis and probabilistic methods requires systematic and detailed formulation of the assessment problem. To facilitate this, a) risk assessors and risk managers should be given training in problem formulation, b) tools to assist appropriate problem formulation should be developed, and c) efforts should be made to develop generic problem formulations (including assessment scenarios, conceptual models, and standard datasets), which can be used as a starting point for assessments of particular pesticides. 

A number of EIA theorists believe in incorporating formal RA methods into EIA as a way to cope with uncertainties, especially in impact prediction where a formal framework for ecological risk assessment (EcoRA) is already developed. It includes three generic phases problem formulation, analysis, and risk characterization followed by risk management. The analysis phase includes an exposure assessment and an ecological effects assessment (see, e.g., US EPA (1998)). 

The frameworks approach also works at the level of problem domain models. The ideal approach is to formulate requirements themselves in a modular fashion by using model frameworks and plugging in the specifics for your problem implementing a code framework solution to the generic problem specification and specializing that implementation framework to construct your system. A typical system consists of numerous such code frameworks and demands careful use of component-based techniques—such as event protocols across frameworks—so that the parts work together correctly. 

Due to the inherent spatial and temporal variability in soils and the resulting uncertainty of generically used standards, it is recommended that there should be few situations for which SQSs are mandatory (i.e., SQSs should not have pass-or-fail criteria in isolation from other considerations). In most cases, SQSs are a first step in a tiered approach or framework for decision making (e.g., Figure 5.1). In each step of the process, the degree of uncertainty decreases, while site specificity, and hence reliability, increases. There are few situations in which SQSs are used as compliance measures, so there is no direct need for strict pass-or-fail criteria. It should be acknowledged that a tiered system nonetheless requires 1) clear criteria associated with each specific tier, which is an issue clearly associated with initial problem formulation, and 2) clear criteria on when to pass to another tier. 

The value of the boundary-integral method is particularly evident if we consider problems in which one or more of the boundaries is a fluid interface. Here, for simplicity, we consider the generic problem of a drop in an unbounded fluid that is undergoing some mean motion that causes the drop to deform in shape. This type of problem is particularly difficult because the shape of the interface is unknown and is often changing with time. We shall see that the boundary-integral formulation provides a powerful basis to attack this class of problems, and in fact, is largely responsible for much of the considerable theoretical progress that has... 

As shown in Fig. 5, each layer considers two independent optimization sections the Solver and the Problem Formulation section. The former regards the optimization algorithm itself, while the latter regards the evaluation of the objective function (i.e., the function to be minimized and the constraints). Within the Generic Optimization layer, there are two abstract upper classes, which are the OptimizationAlgorithm and OptimizationProblem in the Solver and Problem Formulation sections. These two classes are connected in the sense that the OptimizationAlgorithm requires a defined... 

To formulate the generic problems (10.1)-(10.3) in the standard form, the Ui lower bounds must be written in the form (10.6) thus, if the lower bound has a nonzero value, the variable Xi must be opportunely shifted. Moreover, some ... 

In many circumstances, generic substitution is a safe and effective cost-saving tool, but the clinician should be aware of potential problems and, in the event of an unexpected reaction, should ask the patient if the medication has changed in appearance. A change in size, shape, or color, for example, should alert the clinician to a probable change in generic formulation. 

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. 

This book aims at presenting the fundamentals of nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis and chemical engineering. The first chapter introduces the reader to the generic formulations of this class of optimization problems and presents a number of illustrative applications. For the remaining chapters, the book contains the following three main parts ... 

To formulate the problem in a generic form, it can be stated that in an SOFC, the fluid domain is a multi-component system involving chemical reactions, i.e ... 

Mayer Th, May TW, Altenmuller DM, Sandmann M, Wolf P. Chnical problems with generic antiepUeptic drugs. Comparison of sustained release formulations of carbamazepine. Chn Drug Invest 1999 18 17-26. 

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