A collection of models of ``war'' situations were created to demonstate the abilities of disjunctive swarm control. Each one has some variations as to the rules; however, the nature of the disjunctive control is similiar in all of the cases. There are two ``teams'' of agents who are considered to be opponents. These agents exist on a two-dimensional plane using floating-point coordinates between 1 and -1 for both axes. The outside limits prevent the exit of any agent from the playing area.
Each agents is given a strength, a random number between 0 and 1. In most of the models, when two agents come near enough to fight, the agent with the higher strength wins. However, the agent will lose some of its strength in the battle. When not fighting, or close enough to an enemy agent to feel ``threatened'' the strength will slowly increase.
- Bullies Chasing Slowly
- Gang Warfare
- Foxes vs. Rabbits
In this scenario, the speed of a bully towards the nearest dweeb is set proportional to the separating distance, i.e. a bully will run quickly towards a dweeb that is far away, and slowly towards a dweeb nearby. The dweebs are able to find a sweet spot where they can run slowly immediately in front the bully and avoid getting caught. One of the dweebs would typically dance with the bully while the others would hide out of range.
In a second scenario, bullies attack dweebs at a speed independent of their separation. Swarm inversion results in the dweeb strategy of clustering in the center of playing field. The bullies attack causing a scattering of the dweebs. The bullies then concentrate on sacrificial dweebs while other dweebs return to temporary safety in the center. As in the slow chase, the effect was of self sacrifice albeit not as dramatic.
In gang warfare, a second type of wargame, there are two gangs, red and blue, both able to retreat or to attack and kill the other. Each team agent has a randomly assigned strength, and when agents collide the weak is killed and the strongest agent survives. However, the winning agent loses strength. When an agent is killed, the strength of the survivor is decayed by a factor of 0.9. Furthermore, when an agent is far enough away from any enemy agent its strength slowly increases. If the nearest enemy agent is at least 0.1 units away, strength increase by .001 per iteration.
Red does nothing, while blue attacks and then orbits the strong red agents
The blue team evolved a defensive strategy. Instead of attempting to kill the enemy agents, the strategy now prioritizes not getting killed
When given a chance to optimize against the defensive strategy, an aggressive strategy arose. The defensive blue strategy, effective in the remains unchanged. Evolution of the reds, though, has made the blue strategy ineffective.
Foxes vs. rabbits is a third example used to illustrate swarm inversion using disjunctive Combs control. In this model, a bury of rabbits attempts escape to a hole guarded by an earth of predator foxes. Like the war model, each rabbit and fox agent is assigned a strength which determines whether or not it will survive in combat. However, unlike before, strength neither degrades or increases over time. There are 200 foxes and 50 rabbits.
The rabbits rush towards the exit. The rabbits are not actually trying to move towards the hole, but rather away from the foxes. This happens to cause them to move close to the hole, allowing many to escape.
Since the rabbits were running away from the foxes rather then towards the hole, when the foxes were evolved against this behavior they developed a strategy of confusion. The foxes occupy the corners of the area thus keeping the rabbits in the center,
The rabbits were gain evolved. Predictably, the rabbits head towards the target unimpeded while the foxes, still applying their confusion tactics, remain huddled in the corners.
At the end of a rabbit evolution, deception and flanking emerged as a winning strategy. The repeated evolutions resulted in clever rabbit behavior. As the foxes placed themselves between the rabbits and the hole, the rabbits move away from the foxes thereby drawing the foxes further from the hole. The rabbits then sneak little by little around the foxes and make their way to the rabbit hole.
- Animation of how ants use pheromone to get food back to their nest. Click on the animation to drop food. Click Pheromone to see the pheremione stregth. Add ants by ckicking of the lowe rleft. Be prepared to spend your day watching.
- National Geographic article on swarm intelligence.
- Swarming on the Battlefield (Google books)
- Swarm Intelligence in Business Harvard Business Review