"an ant deposits pheromones to
mark trails connecting the nest to food sources [9]."


"for ants to optimize trails
fromthe nest to a food source. It has been suggested that this
happens because larger amounts of pheromones can more
quickly accumulate on the shorter paths, rather than on the
longer ones [2, 3]."



We begin with a description of the so-called �gcentral
nest foraging�h problem: the environment is a nontoroidal
grid world and consists of a nest location and some N food
source locations (for simplicity, our examples will assume
N =1). To be consistent with past literature, we will refer to
our swarm agents as �gants�h. Ants leave the nest in search of
the food sources. From any given square, an ant may move
to any eight-neighbor square which is not occupied by too
many ants (we set the maximum to 10) or does not contain
an obstacle.When it happens upon a food source, the ant becomes
laden with food. When reaching the nest again, the
ant leaves the food at the nest and begins searching again.
The goal is to maximize the rate of food brought to the nest
from the food sources.





dorigos
A formal proof of
the pheromone driven shortest path nding behavior in the general case is missing. Bruckstein et al. [9, 10]
consider the shortest path nding problem in absence of obstacles for ants driven by visual clues and not by
pheromones, and prove the convergence of the ants path to the straight line.