Ant Nest and Ant Pathfinding

Ants are complicated. They are dumb as individuals but they are strong as a society. This is because they have swarm intelligence. To understand their swarm intelligence, we need to know the biological facts about ants first.

Ants are fun

We take a few facts from a comment paper by Jackson and Ratnieks. There are many modes of communications among ants:

• multiple pheromones,
• displays,
• contacts,
• sounds.

Among these modes, pheromones provide shared information among the ants while the ants only need to pay attention to local information. I quote from Jackson et al,

the activities of many ‘agents’ responding only to local information leads to a global adaptive process.

Ant pheromones are diverse. There are many types of pheromones with many different properties. There are at least two dimensions of the pheromone properties, operating time-scale and rewardingness. Some pheromones are volatile (operate within 5min) while some others are less so (lasts 25min or even days). Some pheromones are telling the ants to avoid the path since it is not rewarding while some others operate in the opposite way.

The Shape of the Ant Mound

What is the shape of the ant mound for different ants? Some of them are simply mounds like volcanos while some others are more complicated.

This question might be related to a physics question.

Shape of the Mound

The shape of the mound reflects a principle of minimum energy. If we assume we the sands can be placed in one place, the total energy required would be proportional to the distance from the entrance to the mound, which is a singular point. An equivalent alternative would be a circle around the entrance. Of course, we can not place all the sands on a finite circle or a point, an obvious choice would be a volcano-like mound.

We could also imagine the dynamical evolution of the mound. The mound should grow from a small radius and lower height to a larger radius and higher height.

Pathfinder of Ants

Sometimes they form a line to retrieve the food. Sometimes the lines diverge into different paths. This might be dynamical.

I made a film about this.

In this video, it is quite clear that the ants all follow some certain paths. It is known that the ants

Path Optimization

What is the dynamical path optimization of ants? There is an algorithm called Ant Colony Optimization (ACO) Algorithm.

ACO is a system of algorithms that utilize the ant agents to find the solution of a combinatorial optimization problem. For example, ACO can be used to optimize the paths of the traveling salesman problem.

For simplicity, we consider a simple problem of finding the locations between two locations. We will find a path with minimized distance between the two locations.

The philosophy of an ant agent-based method is to use artificial ants with pheromones.

• Ants move randomly from $A$ to $B$;
• Ants deposit pheromone on their way back from $B$;
• The path preferability for an ant is proportional to the pheromone density;
• The path preferability for an ant is also proportional to the “resistance” of path, e.g., $1/d$ where $d$ is the path distance between the two locations for the specific path.

This problem can also be mapped to a problem on the graph. In this specific problem, we have a graph with two nodes $\{A, B\}$

The Path Diverges

In the video, the path diverges and generates many branches. I can’t know the details from this old clip here but each path may lead to different food sources.