The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
Information Processing Letters
Theoretical Analysis of Initial Particle Swarm Behavior
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Why standard particle swarm optimisers elude a theoretical runtime analysis
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Probability: Theory and Examples
Probability: Theory and Examples
Handbook of Swarm Intelligence: Concepts, Principles and Applications
Handbook of Swarm Intelligence: Concepts, Principles and Applications
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
An approach to multimodal biomedical image registration utilizing particle swarm optimization
IEEE Transactions on Evolutionary Computation
Particles prefer walking along the axes: experimental insights into the behavior of a particle swarm
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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Particle swarm optimization (PSO) is a popular nature-inspired meta-heuristic for solving continuous optimization problems. Although this technique is widely used, up to now only some partial aspects of the method have been formally investigated. In particular, while it is well-studied how to let the swarm converge to a single point in the search space, no general theoretical statements about this point or on the best position any particle has found have been known. For a very general class of objective functions, we provide for the first time results about the quality of the solution found. We show that a slightly adapted PSO almost surely finds a local optimum by investigating the newly defined potential of the swarm. The potential drops when the swarm approaches the point of convergence, but increases if the swarm remains close to a point that is not a local optimum, meaning that the swarm charges potential and continues its movement.