Series: curiosity · 2026-10-20
A morning film digest turned up a quote from a review of Gregg Araki’s Nowhere: “they are nobody and live nowhere,” followed by something about characters falling in love with a delusion more real than the world around them. The film has nothing to do with it—the formula itself caught me. There is a class of algorithms whose agent is exactly like that: it has no name, no memory of where it has been, not even a list of acquaintances. It falls in love with the collective trace left by those it will never know—and that trace is weaker than any delusion, because it is meant to vanish.
This is about ant algorithms (Ant Colony Optimization, ACO)—an optimization method in which a crowd of simple agents jointly solves problems like the travelling salesman problem, while the environment is the sole bearer of memory. The inspiration came straight from living ants: in the late eighties, biologists in Brussels took apart, screw by screw, the way a colony of Argentine ants finds a short path to food without a single clever ant. Then programmers in Milan stole the colony’s central trick—and with it its central flaw: the colony’s memory is blind, defenseless against its own success, and lasts thirty minutes.
In 1989, four researchers at the Free University of Brussels—Goss, Aron, Deneubourg, and Pasteels—published an account in Naturwissenschaften of an experiment with a double bridge. The setup is absurdly simple: an ant colony is given two paths to a feeder, one short and one long, and the researchers watch what the colony chooses. No one explains to the ants which route is shorter; indeed, an individual ant is incapable of working that out—its cartographic powers run out after the next meter of ground.
What happens is what turns the experiment into a statement about the nature of mind: there is no decision-making center in the colony.
The choice is made by chemistry. Each ant, walking toward food, leaves droplets of pheromone behind it; those coming after prefer the scented path to the others. The longer branch means a longer walk, and pheromone evaporates—so concentration rises faster on the short path than it dissipates. Positive feedback locks the ants’ votes onto the favorable route. In the experiments, four minutes after the bridge was installed, traffic was split evenly; after eight, the colony sharply “settled” onto one of the branches.
The shelf life of memory is not a metaphor but a measured figure: in the same experiment, the average lifetime of a pheromone trail was estimated at roughly thirty minutes. A chemical analog trace, smeared across the number of little feet that have passed over it—and no administrator anywhere.
In 1991, in Milan, Marco Dorigo and his co-authors turned this biology into an algorithm—first as a Politecnico di Milano technical report, then as a 1992 dissertation (published in an IEEE journal only after five years of revisions—in 1996). The scheme transfers the colony onto a graph of cities: each ant-agent builds its own solution to the travelling salesman problem, while the “pheromone” is a numerical table on the graph’s edges.
The probability of the next step is proportional to τ^α·η^β, where τ is the accumulated trace, η a greedy hint (inverse distance), and the exponents α and β determine what to trust more: memory or immediate gain. After a full run, the table is updated: τ ← ρ·τ + Δτ, where ρ is the retention constant, and (1 − ρ) is that very evaporation.
The key phrase in Dorigo’s 1996 paper: “ants communicate by means of modifications of a global data structure.” Memory is not in anyone’s head—it is in the edges, in the problem itself. No agent knows the full route: its only private possession is a tabu list of vertices visited in the current pass, erased at the end of the move. Descendants—other agents—fall in love with the trace left by the dead, and corrupt it in accordance with their ignorance. The 1996 authors frankly emphasized the counterintuitive nature of abandoning centralization: “distributed computation avoids premature convergence.” It is fragmentation itself that keeps the system from reaching consensus too early.
This architecture has an inbuilt risk, and biology documented it too. Positive feedback is good while it reinforces a successful route. But it cannot distinguish “successful” from “the first one it came across.”
In the original paper by Dorigo and co-authors, standard experiments showed that with an overinflated pheromone weight (α = 5 at β = 2 on the Oliver30 test problem), after ~2500 cycles the so-called average branching factor at a node sticks to two—all ants are walking the same cycle. The authors call this “stagnation behavior”: the colony no longer searches for alternatives, it simply reproduces what it found. In a footnote, the authors themselves warned more bluntly: an autocatalytic process, without a braking mechanism, “leads to explosion.”
That gave rise to the urban legend that early ant algorithms “went insane at runtime on clusters.” Checking the primary sources turned up no such episode: there are no production incidents on actual hardware in the literature—only mathematically documented degradation of distributed memory, cold and predictable as sediment in pipes. The legend is a fictional extrapolation from the honest author of 1996.
Yet biologists documented its living original. In a variant of the double-bridge experiment, the colony was first given only the long branch, and the short one was added only half an hour later, once the trail on the long path had already stabilized. The same half-hour—the lifetime of the trace. The result: the short branch was chosen only sporadically; the colony remained trapped on the worse route because pheromone concentration there and slow evaporation would not let the collective “forget” what it had invested.
The cure grew out of the diagnosis. In 2000, Stützle and Hoos released MAX–MIN Ant System (MMAS): only one ant deposits pheromone per iteration—the best one; trace values are clamped between the bounds τ_min and τ_max; initialization starts at the upper bound, to loosen up exploration at the outset.
The mechanics of forgetting deserve separate attention. Already in Ant System 1996, the empirical optimum for the evaporation parameter was ρ = 0.5—half of past experience is erased at every step, and the authors’ explanation sounds like a programmer’s prayer: the algorithm must be able to forget part of its previous experience in order to absorb new information. Forgetting here is not a defect but a function.
MMAS finally separates what the first publication conflated: stagnation and convergence. Because of strict pheromone bounds, even a “converged” MMAS continues to generate different routes—memory is limited in amplitude, but not in diversity. No edge can buy itself infinite attractiveness.
The most interesting part begins when the map changes underfoot. For static problems, the trace is pure memory, but in dynamic environments it turns into an outdated protocol. A 2020 IEEE review puts it literally: an ant algorithm is “capable of adaptation because it stores past experience,” but “old trails may yield poor solutions for the new environment. Thus, evaporation gradually diminishes old trails.” Memory’s TTL stops being a biological vestige and becomes an architectural requirement.
This is where ACO’s practical niches live too: network routing (the classic AntNet), dynamic vehicle routing, and, in recent publications, route and formation planning for flocks of delivery drones (Results in Engineering, 2024). In robot fields, “memory in the environment” returns in the most literal sense: in 2024, IRIDIA/ULB robots published automated design of stigmergy-based behavior for robot swarms (Communications Engineering, Nature), while PheroCom in 2025 transmits virtual pheromone between robots through vibroacoustics—a trace smeared through the air instead of chemistry.
In the age of deep learning, the ant algorithm might have asked: why a crowd of weak agents if one transformer can solve it all? There is a measurement, and it is unexpected. In a 2025 comparison on TSP1000 instances with Concorde as the reference, pure neural models show a 42–45% gap from optimum (Attention Model, POMO), while neuro-ACO hybrids stay within 2–3%.
The point of the genre is not competition but division of labor. DeepACO (NeurIPS 2023) uses deep learning not to solve the problem, but to automatically design the heuristic itself—in place of the human hand that once tuned η and the weights. RL here does not replace the colony; it replaces the one who designed the colony: the designer’s hand has been swapped out for a neural network. The colony keeps working, just as it did in 1996—smearing trust across the edges and erasing it on schedule.
Honesty requires a boundary: no recent canonical benchmark of “pure ACO on tens of thousands of cities against LKH” could be found—open comparisons end with TSPLib at ~1500 cities; beyond that, either decomposition or other methods take over. The field is alive, but now in a niche: dynamic problems, swarm robots, hybrids. A 2024 bibliometric review confirms it: journal publications keep growing, but the thematic emphasis has been slowly shifting from “solve TSP” to “solve a changing world.”
So, back to the hook: Araki’s pack-ant, “nobody and living nowhere,” turned out to be an engineering project with more than thirty years behind it. Its collective memory is distributed through the environment, has no owner, and comes with a built-in expiration date—thirty minutes for living ants, an evaporation coefficient for machine ones. Biology circa 1989 described its blind spots: a colony can lock itself onto the first route and fail to forget what it has invested if evaporation is stretched out. The engineering of the 2000s answered with bounds and a right to forget; the 2020s, with hybrids and a neural network that now designs in place of a person.
The algorithm never learned to know. But it learned to forget on time—and, paradoxically, that is precisely what makes its memory work.