Home / Curated / Algorithms / Particle swarm optimization

Particle swarm optimization

Algorithms AIMech:ParticleSwarmOptimization DRAFT

Aliases: PSO

A population-based optimization method that moves candidate particles through a search space using retained velocities and stochastic attraction toward remembered personal and shared best positions.

Identity Notes & Concept Scope This existing continuous PSO identity covers the retained global-best/inertia evidence and the original MHS 1995 local-information variant. The ICNN 1995 simplified rule retains velocity with coefficient 1 and attraction coefficients 2; MHS uses its own ACC_CONST and velocity limits, while the later inertia source is a distinct configuration. It is not differential evolution, an objective-gradient method, a biological flock model, or every discrete, neighborhood or constricted PSO variant. Fresh postmerge collection on 15 October 2026 at base a80a4e53097977b397421562fb1169aa1426dc8b inspected 757 maintained and 442 pinned AIO identities, including 4,789 identity-field occurrences and 3,661 normalized values. Four fixed-string, word-boundary searches included ignored and hidden files in the original checkout and three discovery/recovery checkouts: 8,131, 7,634, 18,826 and 22,178 occurrences, grouped into 3,163 exact contents. Candidate identities had no collision; the four PSO self-matches were explicitly retained for enrichment. Root read 159 decoded candidate contexts (including a separately retained two-context key/value projection correction), all 30 normalized match fields and relevant frontier fields/selected full owner objects. Supporting agents assessed the disjoint candidate and two contextual partitions; full raw-content reconstruction is separate from semantic assessment and is not a claim that root read all raw containers. Existing unrelated definitions, rendered mirrors, historical report/review contexts and incidental substrings do not establish equivalence. The frontier has 909 main and 393 nested objects; only owners 243, 258, 260 and 261 change. This is bounded to the inspected pin, inventories and contexts, not all AI literature or saturation. All four normalized candidate self-matches point to the exact existing ParticleSwarmOptimization record and its retained merged-base preimage, so owner 243 enriches this stable identity instead of creating another record. Its original nine AIO no-match reasons are retained and assessed with the exact pinned class contexts; the initial 285-native identity search remains historical provenance rather than the current denominator. Array-adjacent source neighborhoods are not geometric nearest neighbors or averaged best positions. The 2002 topology recommendations and unresolved operational variants remain outside the added claims.

Claims & Grounded Evidence

3 Claims

Mechanism #method

Initialize a population of real-valued positions and velocities and evaluate the objective. Retain each particle’s best evaluated position and the best position shared across the population. For each coordinate in the inspected global-best rule, add two randomly scaled displacements to the retained velocity: one from the current position toward the personal best and one toward the global best. The baseline is v_new=v+c1*r1*(p−x)+c2*r2*(g−x), followed by x_new=x+v_new; the source gives random factors in [0,1]. Evaluate the resulting positions and refresh the remembered bests when improved. Particles remain population members rather than undergoing target-trial survival selection. In the 1995 simplified version c1=c2=2. The 1999 inertia variant replaces the retained term v by w*v and studies a decreasing w schedule. Initialization, population size, coefficients, velocity limits, boundary treatment, update ordering and stopping rules must be specified for an executable configuration.

supports Source: Particle Swarm Optimization · Locator: Sections3.2–3.7, PDF pp.3–5 / printed1944–1946; Sections5–6, PDF pp.6–7 / printed1947–1948
supports Source: Empirical Study of Particle Swarm Optimization · Locator: Introduction, Equations1a–1b and2a–2b, PDF pp.1–2 / printed1945–1946; experimental settings and discussion/conclusion, PDF pp.3–4 / printed1947–1948

Mechanism #original-local-social-information

In the MHS 1995 local-information variant, each particle retains its own best evaluated position and has access to the best solutions remembered by its array neighbors. A neighborhood best replaces the population-wide best as the social attractor, while the particle retains its velocity and the separate random attraction toward its personal best. The local social input is a selected best remembered position, not the arithmetic average of neighboring positions or a certified optimum near the particle in the objective domain. This changes the information available to the same particle-swarm search mechanism rather than defining a new particle identity or requiring a learned graph.

supports Source: A New Optimizer Using Particle Swarm Theory · Locator: Section 2 continuation and Section 3.1, PDF p. 2 / printed p. 40; Section 3.2, PDF p. 3 / printed p. 41.

Scope #original-array-neighborhood-configurations

The source describes a two-neighbor configuration using the immediately adjacent array positions i-1 and i+1, and a six-neighbor configuration using three positions on each side. It explicitly states wrapped array endpoints for the six-neighbor description. These neighborhoods concern particle-array adjacency, not nearest current positions in the search space. The names neighborhood=2 and neighborhood=6 count the described other array positions; the particle also retains its own personal-best information. These selected configurations do not specify a universal meaning of local-best PSO or a complete implementation for every population size.

supports Source: A New Optimizer Using Particle Swarm Theory · Locator: Section 3.2, PDF p. 3 / printed p. 41, opening neighborhood definitions and the paragraph introducing Table 2.

⚠️ Curated Limitations & Negative Results

Current positions can overshoot remembered bests and have worse objective values. Attraction to a best-so-far position is not attraction to a known global optimum. If every particle has zero velocity and its current position equals both remembered attractors, this displayed rule has no motion; the fixed state need not be optimal.
The original coefficient 1 on old velocity and the later inertia weight must not be conflated. The 1999 experiment’s decreasing weight and Vmax/Xmax settings are particular choices, not universal optimal settings or a complete bound-repair specification. Clipping a velocity alone does not ensure a feasible position.
The full random-stream coupling, synchronous versus asynchronous best updates, ties, constraints and noisy evaluations require declared implementation choices. The social analogy is not a convergence proof. The 1999 discussion explicitly allows failure to find the required optimum; no universal speed, accuracy or finite-budget global-optimum guarantee is asserted.
The MHS local-neighborhood description supplies prose rather than complete local-version pseudocode. An implementation must declare the social-best candidate set and self membership, tie handling, finite-size endpoint conventions and update scheduling. Wrapping is explicit in the six-neighbor passage and is not evidence that every local-best variant uses the same ring. The neighborhood best denotes a remembered evaluated solution; noisy evaluations and uncertainty are not resolved by that selector.
The MHS paper’s apparent immunity of its two-neighbor runs to local optima is an empirical interpretation, not a guarantee of escape or global optimality. If all particles share a nonoptimal position, zero velocity and personal memories at that position, every neighborhood best coincides with it and the displayed attraction rule remains fixed. This is an admissible-state algebraic boundary, not a claim about the probability of that state under a specified initialization. The paper’s comparative observations do not establish a universal ordering of neighborhood sizes or topologies.

Artificial Intelligence Ontology (AIO) Grounding

Explicit AIO Snapshot Assessment: No Match

Rationale: No suitable mapping was found for this general optimization method in the inspected pin. Learning tasks, evolutionary language models, predictive forests, bias concepts and a generic stochastic-process representation do not establish the defining identity. This is a bounded local assessment, not a claim of absence from other ontologies.

Search Scope: Postmerge341 inspection of all 442 pinned AIO and 757 maintained identities (4,789 identity-field occurrences; 3,661 normalized values), four searches including ignored and hidden files, and the attributed candidate/context semantic audit. The existing PSO self-matches are retained explicitly. Nine exact AIO class contexts and the original no-match reasons were reassessed with the accepted PSO audit; relevant optimization, sampling and learning neighbors remain distinct. This updates the current search context, not the historical initial 285-native search or its timestamp, and is bounded to the inspected pin and semantic neighborhoods.

Examined AIO Candidate	Rejection Reason
`AIO:EvolutionaryLLM`	This exact CLASS is a large language model using evolutionary computation. Its related synonym evolutionary algorithms does not denote every stochastic optimizer or establish model equivalence.
`AIO:TrainingStrategy`	The definition concerns preprocessing/training machine-learning models. Optional neural-network or policy optimization applications do not define the full general optimization method.
`AIO:MachineLearningTask`	General objective optimization is not necessarily a task of learning from data as in this target.
`AIO:MetaLearning`	Updating optimizer state or a search distribution is not necessarily learning from metadata about machine-learning experiments.
`AIO:ActiveLearning`	Objective evaluation does not require querying labels for data points.
`AIO:ReinforcementLearning`	These general optimizers do not inherently specify a policy/environment learning task; a possible use in policy search is insufficient.
`AIO:RandomForest`	Neither particle memory nor an adaptive sampling distribution is a predictive decision-tree ensemble.
`AIO:EvaluationBias`	This class describes evaluation population/metric bias rather than an optimization algorithm.
`AIO:MarkovChain`	A possible augmented-state Markov representation is too generic to identify this optimizer. The inspected defining operation is particle motion or elite-distribution refitting, not construction of a target-invariant Markov sampler; the pinned network/model is not an equivalent or necessary semantic parent.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`method-source`	Particle Swarm Optimization James Kennedy, Russell Eberhart	primary paper full_text	ID: doi:10.1109/ICNN.1995.488968 sha256:af61c5180e5d…
`inertia-variant`	Empirical Study of Particle Swarm Optimization Yuhui Shi, Russell C. Eberhart	primary paper full_text	ID: https://staff.washington.edu/paymana/swarm/shi99-cec.pdf sha256:ee6ea14234d0…
`eberhart1995-mhs`	A New Optimizer Using Particle Swarm Theory Russell Eberhart, James Kennedy	primary paper full_text	ID: doi:10.1109/MHS.1995.494215 sha256:b2c926cbd625…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-11T13:05:37Z

Updated: 2026-10-15T13:24:46Z

Source File: data/curated/ParticleSwarmOptimization.yaml