The DOI matches its Crossref record.
The particle swarm - explosion, stability, and convergence in a multidimensional complex space
Abstract
The particle swarm is an algorithm for finding optimal regions of complex search spaces through the interaction of individuals in a population of particles. This paper analyzes a particle's trajectory as it moves in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A five-dimensional depiction is developed, which describes the system completely. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies. Some results of the particle swarm optimizer, implementing modifications derived from the analysis, suggest methods for altering the original algorithm in ways that eliminate problems and increase the ability of the particle swarm to find optima of some well-studied test functions.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Particle swarm optimization: An overview
Poli, R., Kennedy, J., & Blackwell, T. (2007) · Swarm Intelligence · doi:10.1007/s11721-007-0002-0 · Cited by 21,101
Self-citationParticle swarm optimization algorithm: An overview
Wang, D., Tan, D., & Liu, L. (2018) · Soft Computing · doi:10.1007/s00500-016-2474-6 · Cited by 3,343
A Cooperative Approach to Particle Swarm Optimization
vandenBergh, F., & Engelbrecht, A. P. (2004) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2004.826069 · Cited by 2,120
Particle Swarm Optimization: A Comprehensive Survey
Shami, T. M., El-Saleh, A. A., Alswaitti, M., Al-Tashi, Q., Summakieh, M. A., & Mirjalili, S. (2022) · IEEE Access · doi:10.1109/access.2022.3142859 · Cited by 1,584
A Competitive Swarm Optimizer for Large Scale Optimization
Cheng, R., & Jin, Y. (2015) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2014.2322602 · Cited by 1,052
Metadata
- Authors
- Clerc, M., & Kennedy, J.
- Venue
- IEEE Transactions on Evolutionary Computation
- Published
- 2002
- Volume
- 6
- Issue
- 1
- Pages
- 58-73
- ISSN
- 1089-778X (ISSN-L)
- OpenAlex
- W2169245194
- Cited by
- 9,017
- References
- 0
- FWCI
- 85.65
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The particle swarm - explosion, stability, and convergence in a multidimensional complex space. https://app.cochat.ai/papers/10.1109/4235.985692
- The paper
- Clerc, M., & Kennedy, J. (2002). The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation. https://doi.org/10.1109/4235.985692
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
