Particle swarm optimization in high-dimensional bounded search spaces

When applying Particle Swarm Optimization (PSO) to real world optimization problems, often boundary constraints have to be taken into account. In this paper, we will show that the bound handling mechanism essentially influences the swarm behavior, especially in high-dimensional search spaces. In our theoretical analysis, we will prove that all particles are initialized very close to the boundary with overwhelming probability, and that the global guide is expected to leave the search space in every forth dimension. Afterwards, we investigate the initialization process when optimizing the Sphere function, a widely used benchmark, in more detail in order to provide a first step towards explaining previously observed phenomena. Moreover, we will present a broad experimental study of commonly applied bound handling mechanisms on a variety of benchmark functions which is useful for choosing an appropriate strategy in real world applications. Finally, we will derive some guidelines for the practical application of the PSO algorithm in high-dimensional bounded search spaces.