## 1 Introduction  
For many years, designing broad bandwidth antennas has been of significant interest to meet ever increasing demand for a high data rate in wireless communication. In theory, the bandwidth is proportional to the antenna aperture size [1, 2]. However, in the mobile device industry, the allowed antenna volume is often limited by the requirement of mechanical stability and industrial design. For this reason, an inverted-F antenna (IFA) became a commonly used compact design due to its ease of integration and omnidirectional radiation characteristic [3, 4]. There is still a strong demand to increase bandwidth for a given volume. Many useful techniques come from the change in antenna geometry [5], ground plane [6], capacitive loading with several conductive parasitic patches [7], impedance matching circuit [8], substrate permittivity [9], metal chassis [10], etc. However, little has been done in designing an IFA to improve bandwidth using an optimization algorithm. There are many algorithmic methods for optimizing antenna geometries. These optimization algorithms are mainly classified into three categories--deterministic, meta-heuristic (or stochastic), and surrogate model-assisted algorithms [11]. The deterministic algorithms compute each iteration in a search space and find an optimal solution by simply following a simple line based on the previous iteration of best fitness. For this reason, it has a high possibility to become stuck in local maxima or minima [12]. By comparison, the stochastic algorithms utilize random generation of possible solutions at each iteration to increase the chance of exploring the entire search space. These algorithms are further categorized as swarm intelligence-based (SI-based) [13, 14] or non-swarm intelligence-based (non-SI-based) [15, 16] algorithms. The key factor for success in these algorithms is heavily dependent on how thoroughly the search space is explored. Finally, the surrogate model-based algorithms build a substitutional model with multiple pre-simulated data sets to predict solutions [17]. Examples include space mapping [18], shape-preserving response prediction [19], and artificial neural network (ANN) [20]. The SI-based algorithms are bio-inspired evolutionary algorithms and beneficial in the design case where a traditional mathematical method may fail. The genetic algorithm (GA), ant colony optimization (ACO), and particle swarm optimization (PSO) are the mainstream in antenna design. These algorithms utilize a collection of agents traversing the solution space of a cost function, sometimes called the fitness function. An agent's position in the solution space represents a set of parameters in the cost function. An agent's cost is the fitness function evaluated at that agent's position. The objective of GA, ACO, and PSO is to find the global maximum or (in usual practice) global minimum of the cost function. GA does this by utilizing the principles of natural biological evolution and relying on the process of selection, crossover, and mutation [21]. In this process, only 'elite chromosomes' with the lowest costs survive when minimizing. The probability of survival varies with generation and the number of crossovers and mutations. ACO and PSO, by comparison, exploit the behavior of biological entities. ACO mimics the behavior of a colony of foraging ants to seek the path or position that best satisfies the cost function [22; 23]. Some implementations of ACO mimic pheromones to urge agents towards promising solutions [22]. PSO imitates the behavior of a swarm of flying bees looking for food [24]. It does not exchange materials with other particles. Instead, a particle is influenced by its current position, swarm best position, and velocity. The particles are persistent and are not removed throughout the optimization process. Recently, PSO has been utilized in a wide variety of applications in the field of antennas and electromagnetic structures.