Visualizing the Search Dynamics in a High-Dimensional Space for a Particle Swarm Optimizer

Visualization of an evolutionary algorithm may lead to better understanding of how it works. In this paper, three dimension reduction techniques (i.e. PCA, Sammon mapping, and recently developed t-SNE) are compared and analyzed empirically for visualizing the search dynamics of a particle swarm optimizer. Specifically, the search path of the global best position of a particle swarm optimizer over iterations is depicted in a low-dimensional space. Visualization results simulated on a variety of continuous functions show that (1) t-SNE could display the evolution of search path but its performance deteriorates as the dimension increases, and t-SNE tends to enlarge the search path generated during the later search stage; (2) the local search behavior (e.g. convergence to the optimum) can be identified by PCA with more stable performance than its two competitors, though for which it may be difficult to clearly depict the global search path; (3) Sammon mapping suffers easily from the overlapping problem. Furthermore, some important practical issues on how to appropriately interpret visualization results in the low-dimensional space are also highlighted.