Particle swarm optimization in stationary and dynamic environments

Inspired by social behavior of bird flocking or fish schooling, Eberhart and Kennedy first developed the particle swarm optimization (PSO) algorithm in 1995. PSO, as a branch of evolutionary computation, has been successfully applied in many research and application areas in the past several years, e.g., global optimization, artificial neural network training, and fuzzy system control, etc.. Especially, for global optimization, PSO has shown its superior advantages and effectiveness. Although PSO is an effective tool for global optimization problems, it shows weakness while solving complex problems (e.g., shifted, rotated, and compositional problems) or dynamic problems (e.g., the moving peak problem and the DF1 function). This is especially true for the original PSO algorithm. In order to improve the performance of PSO to solve complex problems, we present a novel algorithm, called self-learning PSO (SLPSO). In SLPSO, each particle has four different learning strategies to deal with different situations in the search space. The cooperation of the four learning strategies is implemented by an adaptive framework at the individual level, which can enable each particle to choose the optimal learning strategy according to the properties of its own local fitness landscape. This flexible learning mechanism is able to automatically balance the behavior of exploration and exploitation for each particle in the entire search space during the whole running process. Anothermajor contribution of thiswork is to adapt PSO todynamic environments, we propose an idea that applies hierarchical clustering techniques to generate multiple populations. This idea is the first attempt to solve some open issues when using multiple population methods in dynamic environments, such as, how to define the size of search region of a sub-population, how many individuals are needed in each sub-population, and how many sub-populations are needed, etc.. Experimental study has shown that this idea is effective to locate and track multiple peaks in dynamic environments.