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).

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