ABSTRACT
This chapter presents several optimization methods that are of interest in engineering systems. Geometric programming is a nonlinear optimization technique that requires the objective function and the constraints to be sums of polynomials. Because many thermal systems can be represented by polynomials and power-law expressions with exponents that are positive, negative, fractions, or whole numbers, this technique is of particular value in the optimization of these systems. Linear programming, which is extensively used in industrial engineering, economics, traffic flow, telecommunications, and many other important applications, requires that the objective function and the constraints be linear functions of the variables. Because thermal processes are generally nonlinear, linear programming is not particularly useful for thermal systems. However, some problems may be linear, the equations may be linearized in some cases, or piecewise optimization may be carried out, allowing the use of linear programming. The basic approach for solving linear programming problems is discussed using graphical methods and algebra with slack variables. The frequently used simplex algorithm is also presented. Dynamic programming leads to an optimal function rather than an optimal point. It is applicable to processes that involve several discrete stages or that can be approximated by a series of steps. Thus, it seeks to optimize the path through the various steps. Dynamic programming is of limited interest in typical thermal systems and processes. Similarly, other specialized techniques such as structural, shape, and trajectory optimization are outlined.
