Wikipedia — Artificial bee colony algorithm

Authoritative reference used to deepen artificial-bee-colony with the canonical Karaboga mechanics, independent of andrey-dik‘s MQL5 implementation.

What it adds

Originator. Derviş Karaboğa (Erciyes University), 2005.
Four phases in order: initialization (seed food sources for all employed bees), employed bee phase, onlooker bee phase (“chooses one of their sources depending on the dances”), and scout bee phase (“abandoned food sources … are replaced with the new food sources discovered by scouts”).
Candidate-solution formula. A new position is vᵢₖ = xᵢₖ + Φᵢₖ·(xᵢₖ − xⱼₖ) with Φ random in [−1, 1] and j a randomly chosen other source.
Abandonment parameter. “If a position cannot be improved over a predefined number (called limit) of cycles, then the food source is abandoned” — the limit is the explicit explore/exploit knob.
Onlooker selection. “roulette wheel selection”, fitness-proportional Pᵢ = fitᵢ / Σⱼ fitⱼ.
Colony split. “the first half of the swarm consists of employed bees, and the second half constitutes the onlooker bees.”