Wikipedia — Ant colony optimization algorithms

Authoritative reference used to deepen ant-colony-optimization with the canonical Ant System formulation, independent of andrey-dik‘s continuous MQL5 reimagining.

What it adds

• Provenance. Marco Dorigo proposed the Ant System (AS) in his 1992 PhD thesis (foundational paper 1996).
• Transition rule. Ants pick moves by pˣʸ ∝ (τₓᵧ)^α · (ηₓᵧ)^β, combining the pheromone trail τ (exponent α ≥ 0) and the heuristic desirability η (typically 1/distance, exponent β ≥ 1).
• Pheromone update. τₓᵧ ← (1−ρ)τₓᵧ + Σ Δτₓᵧ, where ρ is the “pheromone evaporation coefficient” that prevents premature convergence.
• Variants. Ant Colony System (ACS), MAX–MIN Ant System (MMAS) (bounds τ to [τ_min, τ_max]), Elitist AS, and rank-based AS_rank.
• Native domain. ACO is for combinatorial optimization on graphs — “the traveling salesman problem remains the canonical application.” (Dik’s MQL5 version is a continuous adaptation, which is off the original target domain.)

Tier T2. Cited from ant-colony-optimization.