Antenna Optimization Using Multiobjective Algorithms

This paper presents several applications of multiobjective optimization to antenna design, emphasizing the main general steps in this process. Specifications of antennas usually involve many conflicting objectives related to directivity, impedance matching, cross-polarization, and frequency range. These requirements induce multiobjective problems, which are formulated, solved, and analyzed here for three distinct antenna designs: a bowtie antenna for ground-penetrating radars, a reflector antenna for satellite broadcast systems, and a meander-line antenna for radio-frequency identification tags. Both stochastic and deterministic methods are considered in the analysis. 1. Introduction Antenna optimization aims at creating advanced and complex electromagnetic devices that must be competitive in terms of performance, serviceability, and cost effectiveness. This process involves selection of appropriate objective functions (usually conflicting), design variables, parameters, and constraints. In most antenna optimization problems, several goals must be satisfied simultaneously in order to obtain an optimal solution. As these objectives are often conflicting, no single solution may exist that is best regarding all considered goals. In many situations, antenna optimization can be viewed as a multidisciplinary engineered problem. However, most of the problems can be divided into search for optimal solutions and approximate solution of Maxwell’s equations using numerical methods. Important features regarding antenna optimization have to be considered: the objective function might have several local minima and its evaluation can be expensive. Of course, trying to find the global minimum can be prohibitive; therefore, using a suitable method for the given problem is fundamental for a proper engineering solution. For instance, some problems have well-established engineering solutions that were achieved after several years of tests and experiments. In such a situation, it may be desired to find a novel design which improves the known standard result, even though it may not be a global minimum. When the gradient or at least one subgradient is known, there are a couple of deterministic methods which can guarantee improvement (if an improved solution exists) of a given result [1]. Nevertheless, conditions where deterministic methods work well may not be achieved and, thus, stochastic methods may become a good alternative. In fact, stochastic methods such as genetic algorithms, particle swarm optimization, and immune systems are known to be very robust and capable of