Synthesis of Planar Arrays Using Particle Swarms with Selection

Abstract

In this work, two well-known classical PSO schemes have been modified by introducing a tournament selection strategy, commonly used in genetic algorithms, and the new hybrid PSO schemes (HPSO) have been applied to planar array synthesis. The classical PSO schemes with either synchronous or asynchronous updates of the swarm and a global topology are considered and appropriately modified by introducing a tournament selection strategy in order to increase search pressure and make the algorithm speed up convergence. Results comparing both classical and HPSO schemes are included and the pros and cons of the hybrid approach proposed are reported and discussed. The synthesis of the complex element weights to best meet certain far-field radiation pattern restrictions given in terms of 3D-masks has been considered as the canonical problem. Furthermore, representative synthesis results for a planar array to be considered as a 120 degrees sectored antenna for local multipoint distribution systems (LMDS) are also included. Modern heuristic optimization methods such as simulated annealing (SA), genetic algorithms (GA), ant colony optimization (ACO) and more recently particle swarm optimization (PSO), have received great attention among the scientific community in many applications and research areas during the last decade, demonstrating throughout the literature its ability to cope with high-dimensional and multimodal optimization problems (1). Among these techniques, the PSO algorithm has gained many practitioners as it turns out to be easier to implement and tune than other population-based methods such as GA, (2-4). The three main advantages of the heuristic PSO algorithm against GA concern the simplicity of implementation, the use of only one operator -the velocity operator- and the smaller number of parameters to be set and tuned. Similar in nature to other stochastic methods, the PSO algorithm emulates computationally the behavior of groups such as bird flocking or fish schooling from the interaction of the individuals among themselves and with the environment (5). Moreover, different classical schemes can be proposed and found in the literature, classified and differentiated depending on how and when the information concerning new promising regions visited by any of the individuals, particles or agents throughout the optimization process, is transmitted to the rest of the swarm, (2, 6). Basically, depending on how the information flows, i.e. the instant the new discoveries or improvements achieved by any particle within the swarm is available for the rest of the population, either synchronous or asynchronous PSO schemes can be considered. Finally, depending on how each particle becomes influenced by the experience acquired by its neighbors, several swarm topologies can be outlined (2, 4, 7), although in this work the global topology is only considered. Similar in some aspects to human cultural behavior, the global topology PSO scheme means that any particle within the swarm directs its search according to the achievements and recent discoveries obtained by any partner within the swarm, even if it points towards deceptive or local solutions. Global topologies are less robust than the local ones, but on the contrary they are slightly faster (2, 4). In an attempt to improve the overall performance of the classical PSO schemes, a hybridized approach introducing