All hydrosystems engineering problems involve many interconnected and interrelated components. The analysis of any hydrosystem problem should take those interactions into account so that the overall behavior of the system is modeled properly. In general, problems in hydrosystems engineering can be classified into (1) development problems, (2) design problems, and (3) operational problems (Buras, 1972). In fact, practically all hydrosystems engineering problems encompass these problem types, which involve activities relating to determination of (1) the optimal scale of development of the project, (2) the optimal dimensions of the various components of the system, and (3) the optimal operation of the system.
Frequently, design and analysis of hydrosystems involve the use of models. The primary objectives of modeling exercises are (1) to analyze the behavior of existing systems so as to improve their performance and (2) to identify the “best” structural components and configurations of a system under planning. As discussed in Chap. 1, owing to the existence of various uncertainties in hydrosystems modeling, one cannot be certain that the best solution obtained is indeed truly optimal. The conventional approach when facing uncertainties in engineering design is to conduct sensitivity analysis, by which the influences of variation in model parameters subject to uncertainty on the system responses are assessed quantitatively. Simple sensitivity analyses often are ineffective in providing design, management, or operational guidance because when the various system parameters are changed systematically in sensitivity analysis, no consideration is given to whether the changed values are likely or realistic. It is therefore the objective of this chapter to present some practical approaches that integrate the uncertainties and reliability in an optimization framework for hydrosystems design, management, and operation.
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This chapter starts with a brief description of the concepts of some frequently used optimization techniques in hydrosystems engineering design, management, and operation. More detailed descriptions of the various optimization techniques are given by Mays and Tung (1992), along with several specialized textbooks on the different subject matters. In Sec. 8.2, focus is placed on some typical problems in the context of resource allocation to optimize system reliability. Then the concept of risk-based design is described in Sec. 8.3, followed by an example application to hydrosystems engineering in Sec. 8.4. The last two sections, Secs. 8.5 and 8.6, describe a simple way to solve an optimization model in which the parameters are subject to uncertainty.
