Chapter 3: Introduction to Numerical Optimization

The primary topic of this book is surrogate-assisted of antenna structures; however, for the convenience of the reader, we provide a brief introduction to numerical optimization. In this chapter, we cover selected conventional single-objective optimization techniques, both gradient-based and derivative-free. Chapter 4 outlines global optimization using population-based metaheuristics. An important terminological distinction should be made here between conventional (or direct) and surrogate-based techniques. In direct methods, the expensive electromagnetic (EM)-simulation antenna model is handled directly in the optimization process, whereas in surrogate-assisted algorithms, majority of the operations are carried out using a fast replacement model (the surrogate) with only occasional reference to the expensive simulations. Figure 3.1 shows a general flow of the direct simulation-driven optimization process. It can be observed that each candidate solution (design) produced by the algorithm is evaluated using a computationally expensive high-fidelity simulation. Clearly, this might become a bottleneck if the number of such evaluations is large…