Abstract-A hierarchical version of the particle swarm optimization (PSO) metaheuristic is introduced in this paper. In the new method called H-PSO, the particles are arranged in a dynamic hierarchy that is used to define a neighborhood structure. Depending on the quality of their so-far best-found solution, the particles move up or down the hierarchy. This gives good particles that move up in the hierarchy a larger influence on the swarm. We introduce a variant of H-PSO, in which the shape of the hierarchy is dynamically adapted during the execution of the algorithm. Another variant is to assign different behavior to the individual particles with respect to their level in the hierarchy. H-PSO and its variants are tested on a commonly used set of optimization functions and are compared to PSO using different standard neighborhood schemes.Index Terms-Author, please supply your own keywords or send a blank e-mail to keywords@ieee.org to receive a list of suggested keywords.

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Abstract. Particle Swarm Optimization (PSO) methods for dynamic function optimization are studied in this paper. We compare dynamic variants of standard PSO and Hierarchical PSO (H-PSO) on different dynamic benchmark functions. Moreover, a new type of hierarchical PSO, called Partitioned H-PSO (PH-PSO), is proposed. In this algorithm the hierarchy is partitioned into several sub-swarms for a limited number of generations after a change occurred. Different methods for determining the time when to rejoin the hierarchy and how to handle the topmost sub-swarm are discussed. The test results show that H-PSO performs significantly better than PSO on all test functions and that the PH-PSO algorithms often perform best on multimodal functions where changes are not too severe.

New Particle Swarm Optimization (PSO) methods for dynamic and noisy function optimization are studied in this paper. The new methods are based on the hierarchical PSO (H-PSO) and a new type of H-PSO algorithm, called Partitioned Hierarchical PSO (PH-PSO). PH-PSO maintains a hierarchy of particles that is partitioned into several sub-swarms for a limited number of generations after a change of the environment occurred. Different methods for determining the best time when to rejoin the sub-swarms and how to handle the topmost sub-swarm are discussed. A standard method for metaheuristics to cope with noise is to use function re-evaluations. To reduce the number of necessary re-evaluations a new method is proposed here which uses the hierarchy to find a subset of particles for which re-evaluations are particularly important. In addition, a new method to detect changes of the optimization function in the presence of noise is presented. It differs from conventional detection methods because it does not require additional function evaluations. Instead it relies on observations of changes that occur within the swarm hierarchy. The new algorithms are compared experimentally on different dynamic and noisy benchmark functions with a variant of standard PSO and H-PSO that are both provided with a change detection and response method.