A modified PSO structure resulting in high exploration ability with convergence guaranteed

Xin Chen, Yangmin Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

155 Citations (Scopus)


Particle swarm optimization (PSO) is a population-based stochastic recursion procedure, which simulates the social behavior of a swarm of ants or a school of fish. Based upon the general representation of individual particles, this paper introduces a decreasing coefficient to the updating principle, so that PSO can be viewed as a regular stochastic approximation algorithm. To improve exploration ability, a random velocity is added to the velocity updating in order to balance exploration behavior and convergence rate with respect to different optimization problems. To emphasize the role of this additional velocity, the modified PSO paradigm is named PSO with controllable random exploration velocity (PSO-CREV). Its convergence is proved using Lyapunov theory on stochastic process. From the proof, some properties brought by the stochastic components are obtained such as "divergence before convergence" and "controllable exploration." Finally, a series of benchmarks is proposed to verify the feasibility of PSO-CREV.
Original languageEnglish
Pages (from-to)1271-1289
Number of pages19
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Issue number5
Publication statusPublished - 1 Oct 2007
Externally publishedYes


  • Lyapunov theory
  • Particle swarm optimization with controllable random exploration velocity (PSO-CREV)
  • Stochastic approximation
  • Supermartingale convergence

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Medicine(all)
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


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