A hierarchical particle swarm optimizer for noisy and dynamic environments

Abstract

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.

A New Particle Swarm Optimization Algorithm for Dynamic Environments

“…Janson and Middendorf proposed HPSO, a tree-like structure hierarchical PSO [14], and reported improvements over standard PSO for dynamic environments. They also suggested Partitioned Hierarchical PSO in which a hierarchy of particles is partitioned into several sub-swarms for a limited number of generations after a change in the environment is detected [15]. Lung and Dumitresc [16] used two collaborating populations of equal size, one swarm is responsible for preserving the diversity of the particles by using a crowding differential evolutionary algorithm [17] while the other keeps track of global optimum with a PSO algorithm.…”

Detecting change and dealing with uncertainty in imperfect evolutionary environments

“…Li and Dam [28] showed that restricting the information exchange and preventing convergence, increases the diversity of the population and gave better performance when dealing with DE. Janson and Middendorf proposed a hierarchical PSO [22], which showed improvements over the standard PSO for dynamic environments. Lung and Dumitresc [33] used an approach that relied on two different swarms.…”

Particle Swarm Optimization With Composite Particles in Dynamic Environments

“…Several mechanisms have been introduced to improve the performance of classic PSO in dynamic environments. These mechanisms include adopting the rediversification scheme when a change is detected [8], maintaining the diversity during the run via repulsion [1] or dynamic network topology [21], [29], and multiswarm schemes [28]. These mechanisms are briefly reviewed below.…”

“…In particular, the investigation of PSO in dynamic environments has become one of the most important applications of SI [2], [21]. However, similar to EAs, classic PSO should be modified to deal with the convergence problem for solving DOPs: Once the swarm has converged, particles lose the ability to track new optima due to the low velocity [2].…”