Ant Colony Optimization (ACO)
ACO simulates ant foraging: ants communicate indirectly via pheromone trails (stigmergy — Grassé, 1959), so good paths self-reinforce. Formalized by Marco Dorigo in his 1992 doctoral thesis for combinatorial problems. Source: andrey-dik's MQL5 implementation, which he calls "a brand new ACO" — reimagined for continuous optimization (no node-sequencing constraint).
How it works
Classic principles: ants probabilistically pick paths by pheromone concentration × heuristic distance; shorter paths get more pheromone; evaporation prevents stagnation. Dik's continuous adaptation moves ants along displacement vectors between positions, with parameters PheromoneEffect (convergence rate), PathLengthEffect (far high-pheromone vs. near exploration), PheromoneRadius (influence radius), and PathDeviation (random per-coordinate exploration). See exploration-vs-exploitation.
Canonical Ant System (Dorigo)
The authoritative reference wikipedia-ant-colony-optimization fixes the original formulation, which
Dik's continuous version departs from. In Dorigo's Ant System (1992 thesis), an ant picks a move with
probability pˣʸ ∝ (τₓᵧ)^α · (ηₓᵧ)^β — the pheromone τ (exponent α) times the heuristic
desirability η (1/distance, exponent β) — and trails update by τ ← (1−ρ)τ + ΣΔτ, with ρ the
evaporation coefficient. Standard variants harden this: Ant Colony System, MAX–MIN Ant System
(which bounds τ to [τ_min, τ_max]), and rank-based AS. Crucially, the canonical ACO is a
combinatorial method — "the traveling salesman problem remains the canonical application" — so Dik's
recast for continuous spaces is off the original target domain, which is worth weighing when reading
its continuous-benchmark scores.
Benchmark (context-relative)
In this article's early scoring, ACO posted 0.54688 and ranked first among the algorithms tested — beating PSO and the random baseline, "particularly excelling on smooth, high-dimensional problems" (0.996 → 0.588 on 2→1000-param Skin), but weaker on discrete Megacity (0.787 → 0.082). Small-field, earlier methodology — not the mature %-of-MAX rating; read as suite-relative (no-free-lunch-theorem, population-optimization-benchmark).
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 Dorigo (1992) 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 · particle-swarm-optimization · artificial-bee-colony · tabu-search · wikipedia-ant-colony-optimization