Computer programs, insight

Power system stability studies can provide some insight into the effects of power failure. The calculations can become tedious if performed manually because of the iterative steps required to obtain satisfactory answers. Therefore, a computer program is used to supply the iterative answers in a short time and with comparable accuracy. 

Although computer programs are now used to perform speciation calculations, examining how these calculations are performed provides important insights into the limitations of the model predictions. Thus, we will step through a small part of the calculation used to generate the results presented in Figure 5.4, which represents the iron... 

All of this development may seem like something that would be best handled by a computer program or just represents a chance to practice one s skill with differential equations. But that is not true. It is important to understand the mathematical foundation of this development to gain insight into practical situations. Let us consider some cases that illustrate this point. 

The particle-in-a-box problem, which we considered qualitatively in Chapter 5, turns out to be one of the very few cases in which Schrodinger s equation can be exactly solved. For almost all realistic atomic and molecular potentials, chemists and physicists have to rely on approximate solutions of Equation 6.8 generated by complex computer programs. The known exact solutions are extremely valuable because of the insight... 

The procedures and calculations described in this chapter provide considerable insight into the factors affecting the conformations of polypeptides and proteins. The computer programs for gramicidin-S, oxytocin, vasopressin, etc., can also be used for larger structures—of the size of ribonuclease and lysozyme—although the required computer time is considerably increased. 

Finding a final solution to problem (6.1) is called a solution process. It usually involves the DM and an analyst. An analyst can be a human being or a computer program. The analyst s role is to support the DM and generate information for the DM. Let us emphasize that the DM is not assumed to know multi-objective optimization theory or methods but (s)he is supposed to be an expert in the problem domain, that is, understand the application considered and have insight into the problem. Based on that, (s)he is supposed to be able to specify preference information related to the objectives considered and different solutions. The DM can be, e.g., a designer. The task of a multi-objective optimization method is to help the DM in finding the most preferred solution as the final one. The most preferred solution is a Pareto optimal solution which is satisfactory for the DM. 

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