Particle Swarm Optimization (PSO)
PSO is the canonical swarm metaheuristic, developed by J. Kennedy & R. Eberhart (1995). A swarm of particles flies through the search space; each particle is pulled toward its own best position (cognitive term) and the swarm's best (social term), with momentum. Source: andrey-dik's MQL5 implementation (plus a modified variant, PSOm).
How it works
Each particle updates velocity then position:
- Velocity:
v(t+1) = w·v(t) + c1·rp·(p − x) + c2·rg·(g − x)—winertia,c1cognitive weight (pull to personal bestp),c2social weight (pull to global bestg),rp/rgrandom in [0,1]. - Position:
x(t+1) = x(t) + v(t+1).
Early iterations disperse to explore; convergence comes from "attracting all particles to the particle with the best solution" (exploit). See exploration-vs-exploitation.
Distinctive weakness
Particles change coordinates with near-unity probability each step, so they "oscillate, at best, somewhere in the local extremum" — Dik flags "fast and premature convergence" and "poor scalability." His PSOm (probabilistic coordinate copying from fitter particles) failed to improve it.
Benchmark (context-relative)
In this article's early scoring (3 functions — Skin/Forest/Megacity — over a small field), PSO scored 0.47695, below the RND random-search baseline (0.51254): strong on smooth low-dim (0.984 on 2-param Skin) but collapsing with dimension (→0.087 on 1000-param). Dik: "very weak and not suitable for optimizing complex and even more so discrete functions." A pointed no-free-lunch-theorem datum — the field's most famous swarm method loses to random search on this suite. Note this is the earlier, small-field methodology, not the mature %-of-MAX rating used for the founding four (see that page's methodology note).
Why T2 (re-tiered 2026-08-25)
Held at T3 since ingest, which graded the venue — MQL5, a broker's community article site — rather than what the page rests on. This page's load-bearing claims are a mechanism description of an algorithm published by Kennedy and Eberhart (1995) and a comparative score, both from andrey-dik, who did not write the algorithm and has no stake in where it lands. That is somebody measuring somebody else's work, which QUALITY.md's ladder puts at T2.
The spoke's standing finding — that in this field the scorer is usually the author — is real and does not apply here; it applies to DOAm, which stays T3 because there Dik is scoring his own modification. The confound that does remain is implementation: Dik re-implements each optimizer in MQL5, so his figure grades his code as much as the method, and his scoring scheme changed mid-series (population-optimization-benchmark). Both stay flagged in prose, where a methodological limit belongs — not in the tier.
Note the floor is unmoved by this: T1 ÷ tiered counts T1 against the same denominator either way, so
the change alters the tier mix and not the spoke's floor of 0.18.
Related
metaheuristic-optimization · exploration-vs-exploitation · population-optimization-benchmark · no-free-lunch-theorem · andrey-dik · grey-wolf-optimizer · ant-colony-optimization