@article {527,
	title = {dPSO-Vis: Topology-based Visualization of Discrete Particle Swarm Optimization},
	journal = {Computer Graphics Forum},
	volume = {32},
	year = {2013},
	pages = {351-360},
	abstract = {Particle swarm optimization (PSO) is a metaheuristic that has been applied successfully to many continuous and combinatorial optimization problems, e.g., in the fields of economics, engineering, and natural sciences. In PSO a swarm of particles moves within a search space in order to find an optimal solution. Unfortunately, it is hard to understand in detail why and how changes in the design of PSO algorithms affect the optimization behavior. Visualizing the particle states could provide substantially better insight into PSO algorithms, but in case of combinatorial optimization problems, it raises the problem of illustrating the discrete states that cannot easily be embedded spatially. We propose a visualization approach to analyze the optimization problem topologically using a landscape metaphor. Therefore, we transform the configuration space of the optimization problem into a barrier landscape that is topologically equivalent. This visualization is augmented by an illustration of the time-dependent states of the particles. The user of our tool {\textemdash} called dPSO-Vis {\textemdash} is able to analyze the swarm{\textquoteright}s behavior within the search space. We illustrate our approach with a brief analysis of a PSO algorithm that predicts the secondary structure of RNA molecules.},
	author = {Sebastian Volke and Martin Middendorf and Mario Hlawitschka and Jens Kasten and Dirk Zeckzer and Gerik Scheuermann}
}
