ABSTRACT
This chapter presents search methods, which constitute one of the most important, versatile, and widely used approaches for optimizing thermal systems. Search methods can be used if the objective function and constraints are continuous functions or if these take on discrete values. Both constrained and unconstrained optimizations can be carried out using search methods. The simplest problem of single-variable unconstrained optimization is considered first. Multivariable problems are often broken down into simpler single-variable problems for which these methods can be used. Efficient elimination methods, such as Fibonacci and dichotomous schemes, are presented. The efficiency of these methods in reducing the interval of uncertainty for a given number of iterative designs is discussed. For multivariable problems, lattice search, univariate search strategy, and hill-climbing techniques, such as steepest ascent, and other gradient-based methods are discussed. However, the gradient-based approach requires the determination of the derivatives of the objective function, which could complicate the solution. Other search strategies are also discussed. Constrained multivariable problems are considered and two approaches, the penalty function method and searching along the constraint, are presented. Examples of the application of search methods to practical thermal systems are finally outlined.
